# 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

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• 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

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• 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