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The rank of the fundamental group of certain hyperbolic 3–manifolds fibering over the circle

Juan Souto

Geometry & Topology Monographs 14 (2008) 505–518

DOI: 10.2140/gtm.2008.14.505

arXiv: math/0503163

Abstract

We determine the rank of the fundamental group of those hyperbolic 3–manifolds fibering over the circle whose monodromy is a sufficiently high power of a pseudo-Anosov map. Moreover, we show that any two generating sets with minimal cardinality are Nielsen equivalent.

Keywords

hyperbolic geometry, Heegaard genus, fundamental group

Mathematical Subject Classification

Primary: 57M50

Secondary: 57M07

References
Publication

Received: 11 April 2006
Revised: 26 December 2006
Accepted: 2 January 2007
Published: 29 April 2008

Authors
Juan Souto
Department of Mathematics
University of Chicago
5734 S University Avenue
Chicago, Ill 60637
USA
www.math.uchicago.edu/~juan