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

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dc.creatorKuno, Yusuke
dc.date2007-11-07
dc.date2008-12-12
dc.date.accessioned2026-07-07T12:11:47Z
dc.date.available2026-07-07T12:11:47Z
dc.descriptionWe 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.
dc.description10 pages; corrected typos
dc.identifierhttps://arxiv.org/abs/0711.0990
dc.identifierhttp://arxiv.org/abs/0711.0990
dc.identifierMathematical Proceedings of the Cambridge Philosophical Society, 146, issue 01, pp. 109-118, 2009
dc.identifierdoi:10.1017/S0305004108001680
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210331
dc.subjectGeometric Topology
dc.subjectComplex Variables
dc.subject57N05, 32G15
dc.titleA combinatorial formula for Earle's twisted 1-cocycle on the mapping class group \mathcal{M}_{g,*}
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