Thin position for 3-manifolds. (English) Zbl 0818.57013

Scharlemann, Martin; Thompson, Abigail

Gordon, Cameron (ed.) et al., Geometric topology. Joint US-Israel workshop on geometric topology, June 10-16, 1992, Technion, Haifa, Israel. Providence, RI: American Mathematical Society. Contemp. Math. 164, 231-238 (1994).

Summary: We define thin position for 3-manifolds, and examine its relation to Heegaard genus and essential surfaces in the manifold. We show that if the width of a manifold is smaller than its Heegaard genus then the manifold contains an essential surface of genus less than the Heegaard genus.
For the entire collection see [Zbl 0794.00024].

MSC:

57N10

Topology of general \(3\)-manifolds (MSC2010)

Keywords:

incompressible surfaces; thin position for 3-manifolds; Heegaard genus; essential surfaces; width of a manifold