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

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**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)

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