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The rank of the fundamental group of certain hyperbolic
3–manifolds fibering over the circle
Juan Souto
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Geometry & Topology Monographs 14
(2008) 505–518
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Abstract
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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.
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Keywords
hyperbolic geometry, Heegaard genus,
fundamental group
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Mathematical Subject Classification
Primary: 57M50
Secondary: 57M07
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Publication
Received: 11 April 2006
Revised: 26 December 2006
Accepted: 2 January 2007
Published: 29 April 2008
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