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

By Mustafa Korkmaz. 2002

84 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/61c185ccc530a66c12a6ae229778010ad472ccd4

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The Picard group of the moduli space of curves with level structures (2009, background): “ers the case g ≥5 and contains an erroneous torsion term. The case g =4 is essentially due to Pitsch [57], though his paper only considers surfaces with boundary. For more information, see the survey [43], which also gives a very short proof (due to Harer) of Theorem 7.1. Theorem 7.3 (Hain, [24]). F”
The First Integral Cohomology of Pure Mapping Class Groups (2017, background): “If the genus is 2, then PMap c ( S ) is the direct limit of groups whose abelianization is ﬁnite and the same argument applies (see [11, Section 5.1.2] or [19, Theorem 5.1]).”