#### Volume 8, issue 3 (2008)

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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
##### Abstract

In this paper we define a ${QP}^{1}$–valued class function on the mapping class group ${\mathsc{ℳ}}_{g,2}$ of a surface ${\Sigma }_{g,2}$ of genus $g$ with two boundary components. Let $E$ be a ${\Sigma }_{g,2}$–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 ${\mathsc{ℳ}}_{g,2}$ defined by the difference of the signature of these two surface bundles over $P$.

##### Keywords
mapping class group, Meyer cocycle, signature cocycle
##### Mathematical Subject Classification 2000
Primary: 57N13, 55R40
Secondary: 57M07