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A combinatorial formula for Earle's twisted 1-cocycle on the mapping class group

Published online by Cambridge University Press:  01 January 2009

YUSUKE KUNO
YUSUKE KUNO*
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba Meguro-ku Tokyo 153-0041, Japan. e-mail: kunotti@ms.u-tokyo.ac.jp
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 1 , January 2009 , pp. 109 - 118
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

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