Algebraic and Geometric Topology 4 (2004), paper no. 3, pages 31-47.

Large embedded balls and Heegaard genus in negative curvature

David Bachman, Daryl Cooper, Matthew E. White

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= 1/2 cosh(r) where r denotes the radius of any isometrically embedded ball in M. Assuming an unpublished result of Pitts and Rubinstein improves this to g 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

AMS subject classification. Primary: 57M50. Secondary: 57M27, 57N16.

DOI: 10.2140/agt.2004.4.31

E-print: arXiv:math.GT/0305290

Submitted: 30 May 2003. (Revised: 21 August 2003.) Accepted: 29 August 2003. Published: 24 January 2004.

Notes on file formats

David Bachman, Daryl Cooper, Matthew E. White

DB and MEW: Mathematics Department, Cal Poly State University
San Luis Obispo, CA 93407

DC: Mathematics Department, University of California
Santa Barbara, CA 93106, USA

Email: dbachman@calpoly.edu, cooper@math.ucsb.edu, mewhite@calpoly.edu

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