Volume 8, issue 3 (2008)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
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 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.

Keywords
mapping class group, Meyer cocycle, signature cocycle
Mathematical Subject Classification 2000
Primary: 57N13, 55R40
Secondary: 57M07
References
Publication
Received: 20 February 2008
Revised: 30 May 2008
Accepted: 2 June 2008
Published: 8 October 2008
Authors
Masatoshi Sato
Graduate School of Mathematical Sciences
The University of Tokyo
3-8-1 Komaba Meguro-ku
Tokyo
153-8914
Japan