Yusuke Kuno
Published 2007-11-07, updated 2008-12-12Version 2
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.
Comments: 10 pages; corrected typos
Journal: Mathematical Proceedings of the Cambridge Philosophical Society, 146, issue 01, pp. 109-118, 2009
The first homology group with twisted coefficients for the mapping class group of a non-orientable surface with boundary
The first homology group with twisted coefficients for the mapping class group of a non-orientable surface of genus three with two boundary components
The twist subgroup of the mapping class group of a nonorientable surface
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