145 research outputs found
A combinatorial formula for Earle's twisted 1-cocycle on the mapping class group \mathcal{M}_{g,*}
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.Comment: 10 pages; corrected typo
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