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Virtual homological spectral radius and mapping torus of pseudo-Anosov maps


Author: Hongbin Sun
Journal: Proc. Amer. Math. Soc. 145 (2017), 4551-4560
MSC (2010): Primary 57M10, 57M27
DOI: https://doi.org/10.1090/proc/13564
Published electronically: May 4, 2017
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Abstract: In this note, we show that if a pseudo-Anosov map $ \phi :S\to S$ admits a finite cover whose action on the first homology has spectral radius greater than $ 1$, then the monodromy of any fibered structure of any finite cover of the mapping torus $ M_{\phi }$ has the same property.


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Additional Information

Hongbin Sun
Affiliation: Department of Mathematics, University of California Berkeley, Berkeley, California 94720
Email: hongbins@math.berkeley.edu, hongbin.sun2331@gmail.com

DOI: https://doi.org/10.1090/proc/13564
Keywords: Pseudo-Anosov maps, fibered $3$-manifolds, Alexander polynomial, Mahler measure.
Received by editor(s): August 28, 2016
Received by editor(s) in revised form: September 27, 2016, October 18, 2016, and October 21, 2016
Published electronically: May 4, 2017
Additional Notes: The author was partially supported by NSF grant No. DMS-1510383.
Communicated by: David Futer
Article copyright: © Copyright 2017 American Mathematical Society