Large embedded balls and Heegaard genus in negative curvature

Details Large embedded balls and Heegaard genus in negative curvature Large embedded balls and Heegaard genus in negative curvature

2003-05-20

arxiv.org/abs/math/0305290v2

Algebr. Geom. Topol. 4 (2004) 31-47

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-3.abs.html

Scientific paper

We show if M is a closed, connected, orientable, hyperbolic 3-manifold with Heegaard genus g then g >= 1/2 cosh(r) where r denotes the radius of any isometrically embedded ball in M. Assuming an unpublished result of Pitts and Rubinstein improves this to g >= 1/2 cosh(r) + 1/2. We also give an upper bound on the volume in terms of the flip distance of a Heegaard splitting, and describe isoperimetric surfaces in hyperbolic balls.

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