Centralizers in Mapping Class Groups and Decidability of Thurston Equivalence
Tóm tắt
We find a constructive bound for the word length of a generating set for the centralizer of an element of the Mapping Class Group. As a consequence, we show that it is algorithmically decidable whether two postcritically finite branched coverings of the sphere are Thurston equivalent.
Tài liệu tham khảo
Bartholdi, L., Buff, X., Graf von Bothmer, H.-C., Kröker, J.: Algorithmic construction of Hurwitz maps, e-print arXiv:1303.1579 (2013)
Bonnot, S., Braverman, M., Yampolsky, M.: Thurston equivalence is decidable. Moscow Math. J. 12, 747–763 (2012)
Bartholdi, L., Dudko, D.: Algorithmic aspects of branched coverings. Ann. Fac. Sci. Toulouse Math. (6) 26(5), 1219–1296 (2017)
Buff, X., Guizhen, C., Lei, T.: Teichmüller spaces and holomorphic dynamics, Handbook of Teichmüller theory. Volume IV, IRMA Lect. Math. Theor. Phys., vol. 19, Eur. Math. Soc., Zürich, pp. 717–756 (2014)
Bowditch, B.H.: Tight geodesics in the curve complex. Invent. Math. 171(2), 281–300 (2008)
Douady, A., Hubbard, J.H.: A proof of Thurston’s topological characterization of rational functions. Acta Math. 171, 263–297 (1993)
Fathi, A., Laudenbach, F., Poénaru, V.: Travaux de Thurston sur les surfaces, Astérisque, vol. 66-67, Société Mathématique de France (1979)
Farb, B., Margalit, D.: A Primer on Mapping Class Groups. Princeton University Press, Princeton
Farb, B., Margalit, D.: A Primer on Mapping Class Groups. Princeton Mathematical Series, vol. 49, Princeton University Press, Princeton, NJ (2012)
Hurwitz, A.: Ueber Riemann’sche Flächen mit gegebenen Verzweigungspunkten. Math. Ann. 39, 1–60 (1891)
McCarthy, J.: Normalizers and centralizers of pseudo-Anosov mapping classes. Preprint (1994)
Maclachlan, C., Harvey, W.J.: On mapping-class groups and Teichmüller spaces. Proc. Lond. Math. Soc. (3) 30(4), 496–512 (1975)
Masur, H.A., Minsky, Y.N.: Geometry of the complex of curves. II. Hierarchical structure. Geom. Funct. Anal. 10(4), 902–974 (2000)
Pilgrim, K.: Canonical Thurston obstructions. Adv. Math. 158(2), 154–168 (2001)
Selinger, N.: Topological characterization of canonical Thurston obstructions. J. Mod. Dyn. 7, 99–117 (2013)
Selinger, N., Yampolsky, M.: Constructive geometrization of Thurston maps and decidability of Thurston equivalence. Arnold Math. J. 1, 361–402 (2015)
Tao, J.: Linearly bounded conjugator property for mapping class groups. Geom. Funct. Anal. 23(1), 415–466 (2013)
Thurston, W.P.: On the geometry and dynamics of diffeomorphisms of surfaces. Bull. Am. Math. Soc. (N.S.) 19(2), 417–431 (1988)
