Skip Navigation


Journal of the London Mathematical Society Advance Access originally published online on October 17, 2007
Journal of the London Mathematical Society 2007 76(2):451-466; doi:10.1112/jlms/jdm077
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
76/2/451    most recent
jdm077v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Moriyama, T.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2007 London Mathematical Society

The mapping class group action on the homology of the configuration spaces of surfaces

Tetsuhiro Moriyama

The Graduate School of Mathematical Sciences
The University of Tokyo
Komaba Meguro-ku
Tokyo 153
Japan

In this paper, we study the natural action of the mapping class group Mg, 1 on the (co)homology groups of the configuration spaces of n-points on a surface {Sigma} of genus g with the boundary {partial}{Sigma} {cong} S1. We present two main results in this paper. The first result is that the kernel of the action of Mg, 1 coincides with the kernel of the natural action on the nth lower central quotient group of the fundamental group of {Sigma}. The second result is a new interpretation of the cohomology group H*(Mg, 1; T[H1]) of Mg, 1 with coefficients in the free tensor algebra T[H1] over Z generated by the first homology group H1 of {Sigma}, by using the configuration spaces. More precisely, we define a certain cochain complex C of Mg, 1-modules by using the configuration spaces and prove that H*(Mg, 1; C) is canonically isomorphic to H*(Mg, 1; T[H1]).

2000 Mathematics Subject Classification 55R80 (primary). 57M05, 20F28 (secondary).

Received October 18, 2006; revised April 3, 2007; published online October 17, 2007.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.