Heegaard splittings of 3-manifolds. (English) Zbl 1044.57006

Li, Benghe (ed.) et al., Low dimensional topology. Lectures presented during the program on low-dimensional topology held at the Morningside Center of Mathematics, Beijing, China, 1998/1999. Somerville, MA: International Press (ISBN 1-57146-112-4/pbk). New Stud. Adv. Math. 3, 25-39 (2003).
This is a short survey article on Heegaard splittings, including examples and exercises which make it suitable as an introduction to the subject. In section two, the basic notions and constructions are introduced, among these Heegaard splittings of 3-manifolds with boundary. In section three, the author studies stabilization and different motions of reducibility. In section four, as an application, he gives a proof of a theorem on the tunnel number of composite knots, which was first given by [M. Scharlemann and J. Schultens, Topology 38, 265–270 (1999; Zbl 0929.57003)].
For the entire collection see [Zbl 1034.57002].


57N10 Topology of general \(3\)-manifolds (MSC2010)
57-02 Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes


Zbl 0929.57003