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The second homology groups of mapping class groups of orientable surfaces

Published online by Cambridge University Press:  02 May 2003

MUSTAFA KORKMAZ
Affiliation:
Department of Mathematics, Middle East Technical University, Ankara, 06531, Turkey. e-mail: [email protected]
ANDRÁS I. STIPSICZ
Affiliation:
Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Réattanoda utca 13-15, Hungary, H-1053. e-mail: [email protected]

Abstract

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.

Type
Research Article
Copyright
2003 Cambridge Philosophical Society

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