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Hyperbolic volume, Heegaard genus and ranks of groups

Peter B Shalen

Geometry & Topology Monographs 12 (2007) 335–349

DOI: 10.2140/gtm.2007.12.335

arXiv: 0904.0191
Abstract

Some conjectures about Heegaard genera and ranks of fundamental groups of 3–manifolds are formulated, and it is shown that they imply new statements about hyperbolic volume.

Keywords

hyperbolic manifold, volume, Heegaard genus, rank of group
Mathematical Subject Classification

Primary: 57M05, 57M50
References
Publication

Received: 29 September 2006
Revised: 27 January 2007
Accepted: 4 March 2007
Published: 3 December 2007
Authors
Peter B Shalen
Department of Mathematics, Statistics, and Computer Science
University of Illinois at Chicago
851 S. Morgan Street
Chicago IL 60607-7045
USA
http://www.math.uic.edu/~shalen/