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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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Algebraic & Geometric Topology 18 (2018) 2471–2495
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Abstract |
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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). |
Keywords
geometric dimension, mapping class group, vc-dimension
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Mathematical Subject Classification 2010
Primary: 20F65, 55R35
Secondary: 20F36
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References |
Publication
Received: 22 August 2017
Revised: 4 January 2018
Accepted: 12 January 2018
Published: 26 April 2018
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Authors |
| Javier Aramayona | |
| ICMAT and Departamento de
Matemáticas Universidad Autónoma de Madrid Ciudad Universitaria de Cantoblanco Madrid Spain |
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| Daniel Juan-Pineda | |
| Centro de Ciencias Matemáticas Universidad Nacional Autónoma de México Morelia Mexico |
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| Alejandra Trujillo-Negrete | |
| Centro de Ciencias Matemáticas Universidad Nacional Autónoma de México Morelia Mexico |
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