A combinatorial formula for Earle's twisted 1-cocycle on the mapping class group \mathcal{M}_{g,*}

Details A combinatorial formula for Earle's twisted 1-cocycle on the mapping class group \mathcal{M}_{g,*} A combinatorial formula for Earle's twisted 1-cocycle on the mapping class group \mathcal{M}_{g,*}

2007-11-07

arxiv.org/abs/0711.0990v2

Mathematical Proceedings of the Cambridge Philosophical Society, 146, issue 01, pp. 109-118, 2009

Mathematics

Geometric Topology

10 pages; corrected typos

Scientific paper

10.1017/S0305004108001680

We present a formula expressing Earle's twisted 1-cocycle on the mapping class group of a closed oriented surface of genus >=2 relative to a fixed base point, with coefficients in the first homology group of the surface. For this purpose we compare it with Morita's twisted 1-cocycle which is combinatorial. The key is the computation of these cocycles on a particular element of the mapping class group, which is topologically a hyperelliptic involution.

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