Geodesic
On the virtually cyclic dimension of mapping class groups of punctured spheres
Aramayona, Javier1 ; Juan-Pineda, Daniel2 ; Trujillo-Negrete, Alejandra2
1 ICMAT and Departamento de Matemáticas, Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, Madrid, Spain
2 Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Morelia, Mexico
Algebraic and Geometric Topology, Tome 18 (2018) no. 4, pp. 2471-2495

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We calculate the virtually cyclic dimension of the mapping class group of a sphere with at most six punctures. As an immediate consequence, we obtain the virtually cyclic dimension of the mapping class group of the twice-holed torus and of the closed genus-two surface.

For spheres with an arbitrary number of punctures, we give a new upper bound for the virtually cyclic dimension of their mapping class group, improving the recent bound of Degrijse and Petrosyan (2015).

DOI : 10.2140/agt.2018.18.2471
Classification : 20F65, 55R35, 20F36
Keywords: geometric dimension, mapping class group, vc-dimension

Aramayona, Javier 1 ; Juan-Pineda, Daniel 2 ; Trujillo-Negrete, Alejandra 2

1 ICMAT and Departamento de Matemáticas, Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, Madrid, Spain
2 Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Morelia, Mexico 
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Aramayona, Javier; Juan-Pineda, Daniel; Trujillo-Negrete, Alejandra. On the virtually cyclic dimension of mapping class groups of punctured spheres. Algebraic and Geometric Topology, Tome 18 (2018) no. 4, pp. 2471-2495. doi: 10.2140/agt.2018.18.2471

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