A combinatorial formula for Earle's twisted 1cocycle on the mapping class group \mathcal{M}_{g,*}
Abstract
We present a formula expressing Earle's twisted 1cocycle 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 1cocycle 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.0990
 Bibcode:
 2007arXiv0711.0990K
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Complex Variables;
 57N05;
 32G15
 EPrint:
 10 pages