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    Kuno, Yusuke Penner, R. C. and Turaev, Vladimir 2013. Marked fatgraph complexes and surface automorphisms. Geometriae Dedicata, Vol. 167, Issue. 1, p. 151.
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A combinatorial formula for Earle's twisted 1-cocycle on the mapping class group

  • YUSUKE KUNO (a1)
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.

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COPYRIGHT: © Cambridge Philosophical Society 2008
References
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[2]Jablow, E. R.Quadratic vector classes on Riemann surfaces. Duke. Math. J. 53, no.1 (1986), 221–232.
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[7]Trapp, R.A linear representation of the mapping class group and the theory of winding numbers. Topology Appl. 43 (1992), 47–64.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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