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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Circular characteristics and fibrations of hyperbolic closed 3-manifolds


Author: Claire Renard
Journal: Proc. Amer. Math. Soc. 142 (2014), 3649-3664
MSC (2010): Primary 57M27; Secondary 57M10, 57M50, 20F67
Published electronically: June 20, 2014
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Abstract: This article provides sufficient conditions for a closed hyperbolic 3-manifold $ M$ with non-zero first Betti number to fiber over the circle, and to find a fiber in $ M$. Those conditions are formulated in terms of the behavior of the circular characteristic in finite regular covers of $ M$. We define the circular characteristic as an invariant associated to a non-trivial cohomology class $ \alpha $ of $ M$, using a Heegaard characteristic.


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Additional Information

Claire Renard
Affiliation: École Normale Supérieure de Cachan, Centre de Mathématiques et de Leurs Applications, 61 avenue du Président Wilson, F-94235 Cachan Cedex, France
Address at time of publication: 24 rue Audollent, 63000 Clermont-Ferrand, France

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-12079-X
PII: S 0002-9939(2014)12079-X
Keywords: Closed 3-manifolds, fibration, finite covers, hyperbolic geometry, handlebodies
Received by editor(s): December 1, 2011
Received by editor(s) in revised form: September 10, 2012, September 24, 2012, and October 25, 2012
Published electronically: June 20, 2014
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.