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.

Read more about Heegaard Splitting:  Definitions, Examples, Theorems, Classifications, History

Other articles related to "heegaard splitting, heegaard splittings, heegaard":

Handle Decomposition - Some Major Theorems and Observations
... A Heegaard splitting of a closed, orientable 3-manifold is a decomposition of a 3-manifold into the union of two (3,1)-handlebodies along their common boundary, called the Heegaard splitting surface ... Heegaard splittings arise for 3-manifolds in several natural ways given a handle decomposition of a 3-manifold, the union of the 0 and 1-handles is a (3,1)-handlebody ... If the 3-manifold has a triangulation T, there is an induced Heegaard splitting where the first (3,1)-handlebody is a regular neighbourhood of the 1-skeleton, and the other (3,1)-handlebody is a regular neighbourhood ...
Heegaard Splitting - History
... The idea of a Heegaard splitting was introduced by Heegaard (1898) ... While Heegaard splittings were studied extensively by mathematicians such as Wolfgang Haken and Friedhelm Waldhausen in the 1960s, it was not until a few decades later that the field was rejuvenated by Casson ...

Famous quotes containing the word splitting:

    Verily, chemistry is not a splitting of hairs when you have got half a dozen raw Irishmen in the laboratory.
    Henry David Thoreau (1817–1862)