Large embedded balls and Heegaard genus in negative curvature
Geometric Topology
2014-10-01 v2
Abstract
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= 1/2 cosh(r) where r denotes the radius of any isometrically embedded ball in M. Assuming an unpublished result of Pitts and Rubinstein improves this to g 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.
Keywords
Cite
@article{arxiv.math/0305290,
title = {Large embedded balls and Heegaard genus in negative curvature},
author = {David Bachman and Daryl Cooper and Matthew E. White},
journal= {arXiv preprint arXiv:math/0305290},
year = {2014}
}
Comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-3.abs.html