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Heegaard Splitting

A Heegaard splitting of a connected orientable 3-Manifold $M$ is any way of expressing $M$ as the Union of two (3,1)-Handlebodies along their boundaries. The boundary of such a (3,1)-Handlebody is an orientable Surface of some Genus, which determines the number of Handles in the (3,1)-Handlebodies. Therefore, the Handlebodies involved in a Heegaard splitting are the same, but they may be glued together in a strange way along their boundary. A diagram showing how the gluing is done is known as a Heegaard Diagram.


Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, p. 255, 1994.

© 1996-9 Eric W. Weisstein