Virtual homological spectral radius and mapping torus of pseudo-Anosov maps
HTML articles powered by AMS MathViewer
- by Hongbin Sun PDF
- Proc. Amer. Math. Soc. 145 (2017), 4551-4560 Request permission
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.References
- Ian Agol, The virtual Haken conjecture, Doc. Math. 18 (2013), 1045–1087. With an appendix by Agol, Daniel Groves, and Jason Manning. MR 3104553
- Ian Agol, Virtual properties of $3$-manifolds, Proceedings of the International Congress of Mathematicians 1 (2014), 141-170.
- David W. Boyd, Kronecker’s theorem and Lehmer’s problem for polynomials in several variables, J. Number Theory 13 (1981), no. 1, 116–121. MR 602452, DOI 10.1016/0022-314X(81)90033-0
- Jérôme Dubois and Yoshikazu Yamaguchi, The twisted Alexander polynomial for finite abelian covers over three manifolds with boundary, Algebr. Geom. Topol. 12 (2012), no. 2, 791–804. MR 2914618, DOI 10.2140/agt.2012.12.791
- Stefan Friedl and Stefano Vidussi, A survey of twisted Alexander polynomials, The mathematics of knots, Contrib. Math. Comput. Sci., vol. 1, Springer, Heidelberg, 2011, pp. 45–94. MR 2777847, DOI 10.1007/978-3-642-15637-3_{3}
- A. Hadari, Every infinite order mapping class has an infinite order action on the homology of some finite cover, available at arXiv:math.GT/1508.01555.
- Thomas Koberda, Asymptotic linearity of the mapping class group and a homological version of the Nielsen-Thurston classification, Geom. Dedicata 156 (2012), 13–30. MR 2863543, DOI 10.1007/s10711-011-9587-y
- Thomas Koberda, Alexander varieties and largeness of finitely presented groups, J. Homotopy Relat. Struct. 9 (2014), no. 2, 513–531. MR 3258692, DOI 10.1007/s40062-013-0037-4
- Thang Le, Homology torsion growth and Mahler measure, Comment. Math. Helv. 89 (2014), no. 3, 719–757. MR 3260847, DOI 10.4171/CMH/332
- Curtis T. McMullen, Polynomial invariants for fibered 3-manifolds and Teichmüller geodesics for foliations, Ann. Sci. École Norm. Sup. (4) 33 (2000), no. 4, 519–560 (English, with English and French summaries). MR 1832823, DOI 10.1016/S0012-9593(00)00121-X
- Curtis T. McMullen, The Alexander polynomial of a 3-manifold and the Thurston norm on cohomology, Ann. Sci. École Norm. Sup. (4) 35 (2002), no. 2, 153–171 (English, with English and French summaries). MR 1914929, DOI 10.1016/S0012-9593(02)01086-8
- Curtis T. McMullen, Entropy on Riemann surfaces and the Jacobians of finite covers, Comment. Math. Helv. 88 (2013), no. 4, 953–964. MR 3134416, DOI 10.4171/CMH/308
- Daniel S. Silver and Susan G. Williams, Mahler measure, links and homology growth, Topology 41 (2002), no. 5, 979–991. MR 1923995, DOI 10.1016/S0040-9383(01)00014-3
- William P. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. (N.S.) 19 (1988), no. 2, 417–431. MR 956596, DOI 10.1090/S0273-0979-1988-15685-6
Additional Information
- Hongbin Sun
- Affiliation: Department of Mathematics, University of California Berkeley, Berkeley, California 94720
- MR Author ID: 898463
- Email: hongbins@math.berkeley.edu, hongbin.sun2331@gmail.com
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 4551-4560
- MSC (2010): Primary 57M10, 57M27
- DOI: https://doi.org/10.1090/proc/13564
- MathSciNet review: 3690637