Minimal dilatation in Penner’s construction
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- by Livio Liechti PDF
- Proc. Amer. Math. Soc. 145 (2017), 3941-3951 Request permission
Abstract:
For all orientable closed surfaces, we determine the minimal dilatation among mapping classes arising from Penner’s construction. We also discuss generalisations to surfaces with punctures.References
- Norbert A’Campo, Sur les valeurs propres de la transformation de Coxeter, Invent. Math. 33 (1976), no. 1, 61–67 (French). MR 424967, DOI 10.1007/BF01425505
- Norbert A’Campo, Planar trees, slalom curves and hyperbolic knots, Inst. Hautes Études Sci. Publ. Math. 88 (1998), 171–180 (1999). MR 1733330
- E. Hironaka, Mapping classes associated to mixed-sign Coxeter graphs, http://arxiv.org/abs/1110.1013.
- Eriko Hironaka and Livio Liechti, On Coxeter mapping classes and fibered alternating links, Michigan Math. J. 65 (2016), no. 4, 799–812. MR 3579186, DOI 10.1307/mmj/1480734020
- Christopher J. Leininger, On groups generated by two positive multi-twists: Teichmüller curves and Lehmer’s number, Geom. Topol. 8 (2004), 1301–1359. MR 2119298, DOI 10.2140/gt.2004.8.1301
- Robert C. Penner, A construction of pseudo-Anosov homeomorphisms, Trans. Amer. Math. Soc. 310 (1988), no. 1, 179–197. MR 930079, DOI 10.1090/S0002-9947-1988-0930079-9
- Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288
- Hyunshik Shin and Balázs Strenner, Pseudo-Anosov mapping classes not arising from Penner’s construction, Geom. Topol. 19 (2015), no. 6, 3645–3656. MR 3447112, DOI 10.2140/gt.2015.19.3645
- Robert Steinberg, Finite reflection groups, Trans. Amer. Math. Soc. 91 (1959), 493–504. MR 106428, DOI 10.1090/S0002-9947-1959-0106428-2
- Balazs Strenner, Algebraic degrees and Galois conjugates of pseudo-Anosov stretch factors, ProQuest LLC, Ann Arbor, MI, 2015. Thesis (Ph.D.)–The University of Wisconsin - Madison. MR 3427250
- 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
- Livio Liechti
- Affiliation: Mathematisches Institut, Universität Bern, Silderstrasse 5, CH-3012 Bern, Switzerland
- MR Author ID: 1151402
- Email: livio.liechti@math.unibe.ch
- Received by editor(s): March 22, 2016
- Received by editor(s) in revised form: September 28, 2016
- Published electronically: May 24, 2017
- Additional Notes: The author was supported by the Swiss National Science Foundation (project no. 159208)
- Communicated by: David Futer
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3941-3951
- MSC (2010): Primary 37E30
- DOI: https://doi.org/10.1090/proc/13521
- MathSciNet review: 3665045