Geodesic
A class function on the mapping class group of an orientable surface and the Meyer cocycle
Sato, Masatoshi1
1Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo, 153-8914, Japan
Algebraic and Geometric Topology, Tome 8 (2008) no. 3, pp. 1647-1665
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In this paper we define a QP1–valued class function on the mapping class group ℳg,2 of a surface Σg,2 of genus g with two boundary components. Let E be a Σg,2–bundle over a pair of pants P. Gluing to E the product of an annulus and P along the boundaries of each fiber, we obtain a closed surface bundle over P. We have another closed surface bundle by gluing to E the product of P and two disks.

The sign of our class function cobounds the 2–cocycle on ℳg,2 defined by the difference of the signature of these two surface bundles over P.

DOI : 10.2140/agt.2008.8.1647
Keywords: mapping class group, Meyer cocycle, signature cocycle

Sato, Masatoshi  1

1 Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo, 153-8914, Japan 
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Sato, Masatoshi. A class function on the mapping class group of an orientable surface and the Meyer cocycle. Algebraic and Geometric Topology, Tome 8 (2008) no. 3, pp. 1647-1665. doi: 10.2140/agt.2008.8.1647

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