Algebraic & Geometric Topology 4 (2004) 31–47

DOI: 10.2140/agt.2004.4.31

Abstract

We show if M is a closed, connected, orientable, hyperbolic 3-manifold with Heegaard genus g then g≥½cosh(r) where r denotes the radius of any isometrically embedded ball in M. Assuming an unpublished result of Pitts and Rubinstein improves this to g≥½cosh(r)+½. 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

Primary: 57M50

Secondary: 57M27, 57N16

References

Publication

Received: 30 May 2003
Revised: 21 August 2003
Accepted: 29 August 2003
Published: 24 January 2004

Authors