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  • Articles  (4)
  • Low Dimensional Geometry and Topology Special Feature  (3)
  • Inaugural Articles, Sustainability Science  (1)
  • National Academy of Sciences  (4)
  • American Society of Hematology
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  • 2011  (4)
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  • 1
    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
    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
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
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  • 3
    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
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
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  • 4
    Publication Date: 2011-01-19
    Description: The crucial role of biodiversity in the links between ecosystems and societies has been repeatedly highlighted both as source of wellbeing and as a target of human actions, but not all aspects of biodiversity are equally important to different ecosystem services. Similarly, different social actors have different perceptions of and access to ecosystem services, and therefore, they have different wants and capacities to select directly or indirectly for particular biodiversity and ecosystem characteristics. Their choices feed back onto the ecosystem services provided to all parties involved and in turn, affect future decisions. Despite this recognition, the research communities addressing biodiversity, ecosystem services, and human outcomes have yet to develop frameworks that adequately treat the multiple dimensions and interactions in the relationship. Here, we present an interdisciplinary framework for the analysis of relationships between functional diversity, ecosystem services, and human actions that is applicable to specific social environmental systems at local scales. We connect the mechanistic understanding of the ecological role of diversity with its social relevance: ecosystem services. The framework permits connections between functional diversity components and priorities of social actors using land use decisions and ecosystem services as the main links between these ecological and social components. We propose a matrix-based method that provides a transparent and flexible platform for quantifying and integrating social and ecological information and negotiating potentially conflicting land uses among multiple social actors. We illustrate the applicability of our framework by way of land use examples from temperate to subtropical South America, an area of rapid social and ecological change.
    Keywords: Inaugural Articles, Sustainability Science
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
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