Geodesic
Centralizers of finite subgroups of the mapping class group
Liang, Hao1
1Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 322 Science and Engineering Offices, 851 S. Morgan Street, Chicago, IL 60607-7045, USA
Algebraic and Geometric Topology, Tome 13 (2013) no. 3, pp. 1513-1530
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

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.

DOI : 10.2140/agt.2013.13.1513
Classification : 20F65, 20F67
Keywords: finite subgroup of mapping class group, curve complex, hyperbolic group, hierarchy

Liang, Hao  1

1 Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 322 Science and Engineering Offices, 851 S. Morgan Street, Chicago, IL 60607-7045, USA 
@article{10_2140_agt_2013_13_1513,
     author = {Liang, Hao},
     title = {Centralizers of finite subgroups of the mapping class group},
     journal = {Algebraic and Geometric Topology},
     pages = {1513--1530},
     year = {2013},
     volume = {13},
     number = {3},
     doi = {10.2140/agt.2013.13.1513},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.1513/}
}
TY  - JOUR
AU  - Liang, Hao
TI  - Centralizers of finite subgroups of the mapping class group
JO  - Algebraic and Geometric Topology
PY  - 2013
SP  - 1513
EP  - 1530
VL  - 13
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.1513/
DO  - 10.2140/agt.2013.13.1513
ID  - 10_2140_agt_2013_13_1513
ER  - 
%0 Journal Article
%A Liang, Hao
%T Centralizers of finite subgroups of the mapping class group
%J Algebraic and Geometric Topology
%D 2013
%P 1513-1530
%V 13
%N 3
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.1513/
%R 10.2140/agt.2013.13.1513
%F 10_2140_agt_2013_13_1513
Liang, Hao. Centralizers of finite subgroups of the mapping class group. Algebraic and Geometric Topology, Tome 13 (2013) no. 3, pp. 1513-1530. doi: 10.2140/agt.2013.13.1513

[1] E Alibegović, Makanin–Razborov diagrams for limit groups, Geom. Topol. 11 (2007) 643

[2] M Bestvina, $\mathbb{R}$–trees in topology, geometry, and group theory, from: "Handbook of geometric topology" (editors R J Daverman, R B Sher), North-Holland (2002) 55

[3] M R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grundl. Math. Wissen. 319, Springer (1999)

[4] J Brock, H Masur, Coarse and synthetic Weil–Petersson geometry: quasi-flats, geodesics and relative hyperbolicity, Geom. Topol. 12 (2008) 2453

[5] B Farb, D Margalit, A primer on mapping class groups, Princeton Mathematical Series 49, Princeton Univ. Press (2012)

[6] D Groves, Limit groups for relatively hyperbolic groups. II. Makanin–Razborov diagrams, Geom. Topol. 9 (2005) 2319

[7] W J Harvey, Boundary structure of the modular group, from: "Riemann surfaces and related topics" (editors I Kra, B Maskit), Ann. of Math. Stud. 97, Princeton Univ. Press (1981) 245

[8] H A Masur, Y N Minsky, Geometry of the complex of curves. I. Hyperbolicity, Invent. Math. 138 (1999) 103

[9] H A Masur, Y N Minsky, Geometry of the complex of curves. II. Hierarchical structure, Geom. Funct. Anal. 10 (2000) 902

[10] E Rips, Z Sela, Structure and rigidity in hyperbolic groups. I, Geom. Funct. Anal. 4 (1994) 337

[11] Z Sela, Acylindrical accessibility for groups, Invent. Math. 129 (1997) 527

[12] J Tao, Linearly bounded conjugator property for mapping class groups, Geom. Funct. Anal. 23 (2013) 415

[13] S A Wolpert, Geodesic length functions and the Nielsen problem, J. Differential Geom. 25 (1987) 275

Cité par Sources :