Algebraic & Geometric Topology

On the virtually cyclic dimension of mapping class groups of punctured spheres

Javier Aramayona, Daniel Juan-Pineda, and Alejandra Trujillo-Negrete

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Abstract

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).

Article information

Source
Algebr. Geom. Topol., Volume 18, Number 4 (2018), 2471-2495.

Dates
Received: 22 August 2017
Revised: 4 January 2018
Accepted: 12 January 2018
First available in Project Euclid: 3 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.agt/1525312835

Digital Object Identifier
doi:10.2140/agt.2018.18.2471

Mathematical Reviews number (MathSciNet)
MR3797073

Zentralblatt MATH identifier
06867664

Subjects
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 55R35: Classifying spaces of groups and $H$-spaces
Secondary: 20F36: Braid groups; Artin groups

Keywords
geometric dimension mapping class group vc-dimension

Citation

Aramayona, Javier; Juan-Pineda, Daniel; Trujillo-Negrete, Alejandra. On the virtually cyclic dimension of mapping class groups of punctured spheres. Algebr. Geom. Topol. 18 (2018), no. 4, 2471--2495. doi:10.2140/agt.2018.18.2471. https://projecteuclid.org/euclid.agt/1525312835


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