A combinatorial formula for Earle's twisted 1-cocycle on the mapping class group \mathcal{M}_{g,*}
arXiv:0711.0990 · doi:10.1017/S0305004108001680
Abstract
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.
10 pages; corrected typos