Heegaard splitting

Heegaard splitting
The decomposition of a 3-manifold as two handlebodies unioned along their boundaries.

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  • Heegaard splitting — In the mathematical field of geometric topology, a Heegaard splitting is a decomposition of a compact oriented 3 manifold that results from dividing it into two handlebodies. The importance of Heegaard splittings has grown in recent years as more …   Wikipedia

  • Heegaard decomposition — noun The decomposition of a 3 manifold as two handlebodies unioned along their boundaries. Syn: Heegaard splitting …   Wiktionary

  • Poul Heegaard — (November 2, 1871 February 7, 1948) was a Danish mathematician active in the field of topology. His 1898 thesis introduced a concept now called the Heegaard splitting of a 3 manifold. Heegaard s ideas allowed him to make a careful critique of… …   Wikipedia

  • Floer homology — is a mathematical tool used in the study of symplectic geometry and low dimensional topology. First introduced by Andreas Floer in his proof of the Arnold conjecture in symplectic geometry, Floer homology is a novel homology theory arising as an… …   Wikipedia

  • 3-manifold — In mathematics, a 3 manifold is a 3 dimensional manifold. The topological, piecewise linear, and smooth categories are all equivalent in three dimensions, so little distinction is usually made in whether we are dealing with say, topological 3… …   Wikipedia

  • Handle decomposition — In mathematics, a handle decomposition of an n manifold M is a representation of that manifold as an exhaustion:M 0 subset M 1 subset dots subset Mwhere each M i is obtained from M {i 1}by attaching a n i handle. Handle decompositions are never… …   Wikipedia

  • Cameron Gordon (mathematician) — Cameron Gordon is a professor of mathematics at the University of Texas at Austin, known for his work in knot theory. Among his notable results is his work with Marc Culler, John Luecke, and Peter Shalen on the cyclic surgery theorem. This was an …   Wikipedia

  • J. Hyam Rubinstein — is a mathematician specializing in low dimensional topology. Having received his Ph.D. from the University of California, Berkeley, in 1974 under the advisorship of John Stallings, he is now a professor and the head of the Department of… …   Wikipedia

  • List of geometric topology topics — This is a list of geometric topology topics, by Wikipedia page. See also: topology glossary List of topology topics List of general topology topics List of algebraic topology topics Publications in topology Contents 1 Low dimensional topology 1.1 …   Wikipedia

  • Low-dimensional topology — In mathematics, low dimensional topology is the branch of topology that studies manifolds of four or fewer dimensions. Representative topics are the structure theory of 3 manifolds and 4 manifolds, knot theory, and braid groups. It can be… …   Wikipedia

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