Mathematical Proceedings of the Cambridge Philosophical Society

Table of Contents - 2003 - Volume 134, Issue 03  


The second homology groups of mapping class groups of orientable surfaces

MUSTAFA KORKMAZ a1 and ANDRÁS I. STIPSICZ a2
a1 Department of Mathematics, Middle East Technical University, Ankara, 06531, Turkey. e-mail: korkmaz@arf.math.metu.edu.tr
a2 Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Réattanoda utca 13-15, Hungary, H-1053. e-mail: stipsicz@renyi.nu

Let $\Sigma_{g,r}^n$ be a connected orientable surface of genus $g$ with $r$ boundary components and $n$ punctures and let $\Gamma_{g,r}^n$ denote the mapping class group of $\Sigma_{g,r}^n$, namely the group of isotopy classes of orientation-preserving diffeomorphisms of $\Sigma_{g,r}^n$ which are the identity on the boundary and on the punctures. Here, we see the punctures on the surface as distinguished points. The isotopies are required to be the identity on the boundary and on the punctures. If $r$ and/or $n$ is zero, then we omit it from the notation.

(Received May 22 2001)
(Revised October 30 2001)