A linear bound on the genera of Heegaard splittings with distances greater than two

Details A linear bound on the genera of Heegaard splittings with distances greater than two A linear bound on the genera of Heegaard splittings with distances greater than two

2008-03-19

arxiv.org/abs/0803.2751v1

Mathematics

Geometric Topology

12pages, 3 figures

Scientific paper

Let N be a closed, orientable 3-manifold that admits a triangulation with t tetrahedra. Let F be a Heegaard surface for N. S. Schleimer showed that if g(F) \geq 2^{2^{16}t^2}, then the Hempel distance of F (denoted by d(F)) is at most two. In this paper we prove the following generalization: Let M be an orientable 3-manifold that admits a generalized triangulation with t generalized tetrahedra. Let S be a Heegaard surface for M. If g(S) \geq 76t+26, then d(S) \leq 2.

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