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  • Low Dimensional Geometry and Topology Special Feature  (2)
  • National Academy of Sciences  (2)
  • Institute of Physics
  • 2010-2014  (2)
  • 1955-1959
  • 1930-1934
  • 2011  (2)
  • 1
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    Low-dimensional topology and geometry [Introductions] (2011)
    National Academy of Sciences
    Details
    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
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
    Published by National Academy of Sciences
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  • 2
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    Fiber-connected, indefinite Morse 2-functions on connected n-manifolds [Mathematics] (2011)
    National Academy of Sciences
    Details
    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
    Published by National Academy of Sciences
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    PAPER CURRENT
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