Algebraic & Geometric Topology

Centralizers of finite subgroups of the mapping class group

Hao Liang

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Abstract

In this paper, we study the action of finite subgroups of the mapping class group of a surface on the curve complex. We prove that if the diameter of the almost fixed point set of a finite subgroup H is big enough, then the centralizer of H is infinite.

Article information

Source
Algebr. Geom. Topol., Volume 13, Number 3 (2013), 1513-1530.

Dates
Received: 24 February 2012
Revised: 11 July 2012
Accepted: 22 December 2012
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715591

Digital Object Identifier
doi:10.2140/agt.2013.13.1513

Mathematical Reviews number (MathSciNet)
MR3071134

Zentralblatt MATH identifier
1295.20042

Subjects
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F67: Hyperbolic groups and nonpositively curved groups

Keywords
finite subgroup of mapping class group curve complex hyperbolic group hierarchy

Citation

Liang, Hao. Centralizers of finite subgroups of the mapping class group. Algebr. Geom. Topol. 13 (2013), no. 3, 1513--1530. doi:10.2140/agt.2013.13.1513. https://projecteuclid.org/euclid.agt/1513715591


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References

  • E Alibegović, Makanin–Razborov diagrams for limit groups, Geom. Topol. 11 (2007) 643–666
  • M Bestvina, $\mathbb{R}$–trees in topology, geometry, and group theory, from: “Handbook of geometric topology”, (R J Daverman, R B Sher, editors), North-Holland, Amsterdam (2002) 55–91
  • M R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grundl. Math. Wissen. 319, Springer, Berlin (1999)
  • J Brock, H Masur, Coarse and synthetic Weil–Petersson geometry: quasi-flats, geodesics and relative hyperbolicity, Geom. Topol. 12 (2008) 2453–2495
  • B Farb, D Margalit, A primer on mapping class groups, Princeton Mathematical Series 49, Princeton Univ. Press (2012)
  • D Groves, Limit groups for relatively hyperbolic groups. II. Makanin–Razborov diagrams, Geom. Topol. 9 (2005) 2319–2358
  • W J Harvey, Boundary structure of the modular group, from: “Riemann surfaces and related topics”, (I Kra, B Maskit, editors), Ann. of Math. Stud. 97, Princeton Univ. Press (1981) 245–251
  • H A Masur, Y N Minsky, Geometry of the complex of curves. I. Hyperbolicity, Invent. Math. 138 (1999) 103–149
  • H A Masur, Y N Minsky, Geometry of the complex of curves. II. Hierarchical structure, Geom. Funct. Anal. 10 (2000) 902–974
  • E Rips, Z Sela, Structure and rigidity in hyperbolic groups. I, Geom. Funct. Anal. 4 (1994) 337–371
  • Z Sela, Acylindrical accessibility for groups, Invent. Math. 129 (1997) 527–565
  • \bibmarginparfound published paper J Tao, Linearly bounded conjugator property for mapping class groups, Geom. Funct. Anal. 23 (2013) 415–466
  • S A Wolpert, Geodesic length functions and the Nielsen problem, J. Differential Geom. 25 (1987) 275–296