Low-dimensional homology groups of mapping class groups: a survey

2003/07/09 by Mustafa Korkmaz · 3 citations
Mathematics · #math.GT

paper · pdf

published as Proceedings of 8th Gokova Geometry-Topology Conference, Turkish Journal of Mathematics 26 no. 1 (2002), 101-114 · 14 pages, 4 figures

arxiv created 2003/07/09 · arxiv updated 2009/12/01

Abstract

In this survey paper, we give a complete list of known results on the first and the second homology groups of surface mapping class groups. Some known results on higher (co)homology are also mentioned.

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• Lower bounds for faithful linear representations of subgroups of the mapping class group
• Global fixed point in low-dimensional surface group deformation space
• A Lefschetz decomposition over \mathbb Z, and applications

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