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A class function on the mapping class group of an orientable surface and the Meyer cocycle

Masatoshi Sato

Algebraic & Geometric Topology 8 (2008) 1647–1665

In this paper we define a QP1–valued class function on the mapping class group g,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 g,2 defined by the difference of the signature of these two surface bundles over P.

mapping class group, Meyer cocycle, signature cocycle
Mathematical Subject Classification 2000
Primary: 57N13, 55R40
Secondary: 57M07
Received: 20 February 2008
Revised: 30 May 2008
Accepted: 2 June 2008
Published: 8 October 2008
Masatoshi Sato
Graduate School of Mathematical Sciences
The University of Tokyo
3-8-1 Komaba Meguro-ku