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  • Low Dimensional Geometry and Topology Special Feature  (10)
  • Cosmochemistry Special Feature  (8)
  • National Academy of Sciences  (18)
  • American Chemical Society
  • American Institute of Physics
  • 2010-2014  (18)
  • 1980-1984
  • 1950-1954
  • 2011  (18)
  • 1950
Collection
Keywords
Publisher
  • National Academy of Sciences  (18)
  • American Chemical Society
  • American Institute of Physics
Years
  • 2010-2014  (18)
  • 1980-1984
  • 1950-1954
Year
  • 2011  (18)
  • 1950
  • 1
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    Tour of bordered Floer theory [Mathematics] (2011)
    National Academy of Sciences
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    Publication Date: 2011-05-18
    Description: Heegaard Floer theory is a kind of topological quantum field theory (TQFT), assigning graded groups to closed, connected, oriented 3-manifolds and group homomorphisms to smooth, oriented four-dimensional cobordisms. Bordered Heegaard Floer homology is an extension of Heegaard Floer homology to 3-manifolds with boundary, with extended-TQFT-type gluing properties. In this survey, we explain the formal structure and construction of bordered Floer homology and sketch how it can be used to compute some aspects of Heegaard Floer theory.
    Keywords: Low Dimensional Geometry and Topology Special Feature
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
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  • 2
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    Recent progress on symplectic embedding problems in four dimensions [Mathematics] (2011)
    National Academy of Sciences
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    Publication Date: 2011-05-18
    Description: We survey some recent progress on understanding when one four-dimensional symplectic manifold can be symplectically embedded into another. In 2010, McDuff established a number-theoretic criterion for the existence of a symplectic embedding of one four-dimensional ellipsoid into another. This result is related to previously known criteria for when a disjoint union of balls can be symplectically embedded into a ball. Numerical invariants defined using embedded contact homology give general obstructions to symplectic embeddings in four dimensions which turn out to be sharp in the above cases.
    Keywords: Low Dimensional Geometry and Topology Special Feature
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  • 3
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    Topology of surface diagrams of smooth 4-manifolds [Mathematics] (2011)
    National Academy of Sciences
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    Publication Date: 2011-05-18
    Description: Surface diagrams are a new way to specify any smooth closed orientable 4-manifold by an orientable surface decorated with simple closed curves. These curves are cyclically indexed, and each curve has a unique transverse intersection with the next. The aim of this paper is to announce a uniqueness theorem for these objects (within a fixed homotopy class) that turns out to be similar to the Reidemeister-Singer theorem for Heegaard splittings of 3-manifolds.
    Keywords: Low Dimensional Geometry and Topology Special Feature
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  • 4
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    Symplectic homology product via Legendrian surgery [Mathematics] (2011)
    National Academy of Sciences
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    Publication Date: 2011-05-18
    Description: This research announcement continues the study of the symplectic homology of Weinstein manifolds undertaken by the authors [Bourgeois F, Ekholm T, Eliashberg Y (2009) arXiv:0911.0026] where the symplectic homology, as a vector space, was expressed in terms of the Legendrian homology algebra of the attaching spheres of critical handles. Here, we express the product and Batalin–Vilkovisky operator of symplectic homology in that context.
    Keywords: Low Dimensional Geometry and Topology Special Feature
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  • 5
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    Establishing a molecular relationship between chondritic and cometary organic solids [Astronomy] (2011)
    National Academy of Sciences
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    Publication Date: 2011-11-30
    Description: Multidimensional solid-state NMR spectroscopy is used to refine the identification and abundance determination of functional groups in insoluble organic matter (IOM) isolated from a carbonaceous chondrite (Murchison, CM2). It is shown that IOM is composed primarily of highly substituted single ring aromatics, substituted furan/pyran moieties, highly branched oxygenated aliphatics, and carbonyl groups. A pathway for producing an IOM-like molecular structure through formaldehyde polymerization is proposed and tested experimentally. Solid-state 13C NMR analysis of aqueously altered formaldehyde polymer reveals considerable similarity with chondritic IOM. Carbon X-ray absorption near edge structure spectroscopy of formaldehyde polymer reveals the presence of similar functional groups across certain Comet 81P/Wild 2 organic solids, interplanetary dust particles, and primitive IOM. Variation in functional group concentration amongst these extraterrestrial materials is understood to be a result of various degrees of processing in the parent bodies, in space, during atmospheric entry, etc. These results support the hypothesis that chondritic IOM and cometary refractory organic solids are related chemically and likely were derived from formaldehyde polymer. The fine-scale morphology of formaldehyde polymer produced in the experiment reveals abundant nanospherules that are similar in size and shape to organic nanoglobules that are ubiquitous in primitive chondrites.
    Keywords: Cosmochemistry Special Feature
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  • 6
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    Terrestrial planet formation [Astronomy] (2011)
    National Academy of Sciences
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    Publication Date: 2011-11-30
    Description: Advances in our understanding of terrestrial planet formation have come from a multidisciplinary approach. Studies of the ages and compositions of primitive meteorites with compositions similar to the Sun have helped to constrain the nature of the building blocks of planets. This information helps to guide numerical models for the three stages of planet formation from dust to planetesimals (∼106 y), followed by planetesimals to embryos (lunar to Mars-sized objects; few × 106 y), and finally embryos to planets (107–108 y). Defining the role of turbulence in the early nebula is a key to understanding the growth of solids larger than meter size. The initiation of runaway growth of embryos from planetesimals ultimately leads to the growth of large terrestrial planets via large impacts. Dynamical models can produce inner Solar System configurations that closely resemble our Solar System, especially when the orbital effects of large planets (Jupiter and Saturn) and damping mechanisms, such as gas drag, are included. Experimental studies of terrestrial planet interiors provide additional constraints on the conditions of differentiation and, therefore, origin. A more complete understanding of terrestrial planet formation might be possible via a combination of chemical and physical modeling, as well as obtaining samples and new geophysical data from other planets (Venus, Mars, or Mercury) and asteroids.
    Keywords: Cosmochemistry Special Feature
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  • 7
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    Laboratory technology and cosmochemistry [Reviews] (2011)
    National Academy of Sciences
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    Publication Date: 2011-11-30
    Description: Recent developments in analytical instrumentation have led to revolutionary discoveries in cosmochemistry. Instrumental advances have been made along two lines: (i) increase in spatial resolution and sensitivity of detection, allowing for the study of increasingly smaller samples, and (ii) increase in the precision of isotopic analysis that allows more precise dating, the study of isotopic heterogeneity in the Solar System, and other studies. A variety of instrumental techniques are discussed, and important examples of discoveries are listed. Instrumental techniques and instruments include the ion microprobe, laser ablation gas MS, Auger EM, resonance ionization MS, accelerator MS, transmission EM, focused ion-beam microscopy, atom probe tomography, X-ray absorption near-edge structure/electron loss near-edge spectroscopy, Raman microprobe, NMR spectroscopy, and inductively coupled plasma MS.
    Keywords: Cosmochemistry Special Feature
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  • 8
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    Spacecraft instrument technology and cosmochemistry [Chemistry] (2011)
    National Academy of Sciences
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    Publication Date: 2011-11-30
    Description: Measurements by instruments on spacecraft have significantly advanced cosmochemistry. Spacecraft missions impose serious limitations on instrument volume, mass, and power, so adaptation of laboratory instruments drives technology. We describe three examples of flight instruments that collected cosmochemical data. Element analyses by Alpha Particle X-ray Spectrometers on the Mars Exploration Rovers have revealed the nature of volcanic rocks and sedimentary deposits on Mars. The Gamma Ray Spectrometer on the Lunar Prospector orbiter provided a global database of element abundances that resulted in a new understanding of the Moon’s crust. The Ion and Neutral Mass Spectrometer on Cassini has analyzed the chemical compositions of the atmosphere of Titan and active plumes on Enceladus.
    Keywords: Cosmochemistry Special Feature
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  • 9
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    Solar composition from the Genesis Discovery Mission [Geophysics] (2011)
    National Academy of Sciences
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    Publication Date: 2011-11-30
    Description: Science results from the Genesis Mission illustrate the major advantages of sample return missions. (i) Important results not otherwise obtainable except by analysis in terrestrial laboratories: the isotopic compositions of O, N, and noble gases differ in the Sun from other inner solar system objects. The N isotopic composition is the same as that of Jupiter. Genesis has resolved discrepancies in the noble gas data from solar wind implanted in lunar soils. (ii) The most advanced analytical instruments have been applied to Genesis samples, including some developed specifically for the mission. (iii) The N isotope result has been replicated with four different instruments.
    Keywords: Cosmochemistry Special Feature
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  • 10
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    Combining meteorites and missions to explore Mars [Geology] (2011)
    National Academy of Sciences
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    Publication Date: 2011-11-30
    Description: Laboratory studies of meteorites and robotic exploration of Mars reveal scant atmosphere, no evidence of plate tectonics, past evidence for abundant water, and a protracted igneous evolution. Despite indirect hints, direct evidence of a martian origin came with the discovery of trapped atmospheric gases in one meteorite. Since then, the study of martian meteorites and findings from missions have been linked. Although the meteorite source locations are unknown, impact ejection modeling and spectral mapping of Mars suggest derivation from small craters in terrains of Amazonian to Hesperian age. Whereas most martian meteorites are young (  4.5 Ga and formation of enriched and depleted reservoirs. However, the history inferred from martian meteorites conflicts with results from recent Mars missions, calling into doubt whether the igneous histor y inferred from the meteorites is applicable to Mars as a whole. Allan Hills 84001 dates to 4.09 Ga and contains fluid-deposited carbonates. Accompanying debate about the mechanism and temperature of origin of the carbonates came several features suggestive of past microbial life in the carbonates. Although highly disputed, the suggestion spurred interest in habitable extreme environments on Earth and throughout the Solar System. A flotilla of subsequent spacecraft has redefined Mars from a volcanic planet to a hydrologically active planet that may have harbored life. Understanding the history and habitability of Mars depends on understanding the coupling of the atmosphere, surface, and subsurface. Sample return that brings back direct evidence from these diverse reservoirs is essential.
    Keywords: Cosmochemistry Special Feature
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  • 11
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    Cosmochemistry: Understanding the Solar System through analysis of extraterrestrial materials [Introductions] (2011)
    National Academy of Sciences
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    Publication Date: 2011-11-30
    Description: Cosmochemistry is the chemical analysis of extraterrestrial materials. This term generally is taken to mean laboratory analysis, which is the cosmochemistry gold standard because of the ability for repeated analysis under highly controlled conditions using the most advanced instrumentation unhindered by limitations in power, space, or environment. Over the past 40 y, advances in technology have enabled telescopic and spacecraft instruments to provide important data that significantly complement the laboratory data. In this special edition, recent advances in the state of the art of cosmochemistry are presented, which range from instrumental analysis of meteorites to theoretical–computational and astronomical observations.
    Keywords: Cosmochemistry Special Feature
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  • 12
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    Stardust in meteorites [Astronomy] (2011)
    National Academy of Sciences
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    Publication Date: 2011-11-30
    Description: Primitive meteorites, interplanetary dust particles, and comets contain dust grains that formed around stars that lived their lives before the solar system formed. These remarkable objects have been intensively studied since their discovery a little over twenty years ago and they provide samples of other stars that can be studied in the laboratory in exquisite detail with modern analytical tools. The properties of stardust grains are used to constrain models of nucleosynthesis in red giant stars and supernovae, the dominant sources of dust grains that are recycled into the interstellar medium by stars.
    Keywords: Cosmochemistry Special Feature
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  • 13
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    Equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions [Mathematics] (2011)
    National Academy of Sciences
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    Publication Date: 2011-05-18
    Description: We sketch the proof of the equivalence between the hat versions of Heegaard Floer homology and embedded contact homology (ECH). The key point is to express these two Floer homology theories in terms of an open book decomposition of the ambient manifold.
    Keywords: Low Dimensional Geometry and Topology Special Feature
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  • 14
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    Low-dimensional topology and geometry [Introductions] (2011)
    National Academy of Sciences
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    Publication Date: 2011-05-18
    Description: At the core of low-dimensional topology has been the classification of knots and links in the 3-sphere and the classification of 3- and 4-dimensional manifolds (see Wikipedia for the definitions of basic topological terms). Beginning with the introduction of hyperbolic geometry into knots and 3-manifolds by W. Thurston in the late 1970s, geometric tools have become vital to the subject.Next came Freedman's (1) classification of simply connected topological 4-manifolds in 1981 followed by the gauge theory invariants of smooth 4-manifolds introduced by Donaldson (2) in 1982. The gauge theory invariants (2) were based on solutions to the Yang–Mills equations for...
    Keywords: Low Dimensional Geometry and Topology Special Feature
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  • 15
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    Fukaya categories of the torus and Dehn surgery [Mathematics] (2011)
    National Academy of Sciences
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    Publication Date: 2011-05-18
    Description: This paper is a companion to the authors’ forthcoming work extending Heegaard Floer theory from closed 3-manifolds to compact 3-manifolds with two boundary components via quilted Floer cohomology. We describe the first interesting case of this theory: the invariants of 3-manifolds bounding , regarded as modules over the Fukaya category of the punctured 2-torus. We extract a short proof of exactness of the Dehn surgery triangle in Heegaard Floer homology. We show that A∞-structures on the graded algebra A formed by the cohomology of two basic objects in the Fukaya category of the punctured 2-torus are governed by just two parameters (m6, m8), extracted from the Hochschild cohomology of A. For the Fukaya category itself, m6 ≠ 0.
    Keywords: Low Dimensional Geometry and Topology Special Feature
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  • 16
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    Fiber-connected, indefinite Morse 2-functions on connected n-manifolds [Mathematics] (2011)
    National Academy of Sciences
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    Publication Date: 2011-05-18
    Description: We discuss generic smooth maps from smooth manifolds to smooth surfaces, which we call “Morse 2-functions,” and homotopies between such maps. The two central issues are to keep the fibers connected, in which case the Morse 2-function is “fiber-connected,” and to avoid local extrema over one-dimensional submanifolds of the range, in which case the Morse 2-function is “indefinite.” This is foundational work for the long-range goal of defining smooth invariants from Morse 2-functions using tools analogous to classical Morse homology and Cerf theory.
    Keywords: Low Dimensional Geometry and Topology Special Feature
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  • 17
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    Higher categories, colimits, and the blob complex [Mathematics] (2011)
    National Academy of Sciences
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    Publication Date: 2011-05-18
    Description: We summarize our axioms for higher categories, and describe the “blob complex.” Fixing an n-category , the blob complex associates a chain complex to any n-manifold W. The zeroth homology of this chain complex recovers the usual topological quantum field theory invariants of W. The higher homology groups should be viewed as generalizations of Hochschild homology (indeed, when W = S1, they coincide). The blob complex has a very natural definition in terms of homotopy colimits along decompositions of the manifold W. We outline the important properties of the blob complex and sketch the proof of a generalization of Deligne’s conjecture on Hochschild cohomology and the little discs operad to higher dimensions.
    Keywords: Low Dimensional Geometry and Topology Special Feature
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  • 18
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    Higher-order intersections in low-dimensional topology [Mathematics] (2011)
    National Academy of Sciences
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    Publication Date: 2011-05-18
    Description: We show how to measure the failure of the Whitney move in dimension 4 by constructing higher-order intersection invariants of Whitney towers built from iterated Whitney disks on immersed surfaces in 4-manifolds. For Whitney towers on immersed disks in the 4-ball, we identify some of these new invariants with previously known link invariants such as Milnor, Sato–Levine, and Arf invariants. We also define higher-order Sato–Levine and Arf invariants and show that these invariants detect the obstructions to framing a twisted Whitney tower. Together with Milnor invariants, these higher-order invariants are shown to classify the existence of (twisted) Whitney towers of increasing order in the 4-ball. A conjecture regarding the nontriviality of the higher-order Arf invariants is formulated, and related implications for filtrations of string links and 3-dimensional homology cylinders are described.
    Keywords: Low Dimensional Geometry and Topology Special Feature
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