Volume 4, issue 1 (2004)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Large embedded balls and Heegaard genus in negative curvature

David Bachman, Daryl Cooper and Matthew E White

Algebraic & Geometric Topology 4 (2004) 31–47

arXiv: math.GT/0305290

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Heegaard genus g then g 1 2 cosh(r) where r denotes the radius of any isometrically embedded ball in M. Assuming an unpublished result of Pitts and Rubinstein improves this to g 1 2 cosh(r) + 1 2.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
Heegaard splitting, injectivity radius
Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 57M27, 57N16
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Publication
Received: 30 May 2003
Revised: 21 August 2003
Accepted: 29 August 2003
Published: 24 January 2004
Authors
David Bachman
Mathematics Department
Cal Poly State University
San Luis Obispo CA 93407
USA
Daryl Cooper
Mathematics Department
University of California
Santa Barbara CA 93106
USA
Matthew E White
Mathematics Department
Cal Poly State University
San Luis Obispo CA 93407
USA