On the stable cohomology algebra of extended mapping class groups for surfaces

Kawazumi, N.

Hokkaido University Preprint Series in Mathematics, 1995, 311, 1-13

Permalink : https://doi.org/10.14943/83458

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DOI	https://doi.org/10.14943/83458
URI	https://hdl.handle.net/2115/69062
タイトル	On the stable cohomology algebra of extended mapping class groups for surfaces
著者	著者名 Kawazumi, N.
言語	英語
発行日	1995-10-01
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	311
ページ	1-13
抄録	Let :E0,1 be an oriented compact surface of genus g with 1 boundary component, and r g,1 the mapping·class group of :Eg,1 · We determine the stable cohomology group of r 0,1 with coefficients in H1 (:Eg,1; Z)®n, n 􀀥 l, explicitly modulo the stable cohomology group with trivial coefficients. As a corollary the rational stable cohomology algebra of the semi-direct product r g,1 1>< H1 (:E0,1; Z) (which we call the extended mapping class group) is proved to be freely generated by the generalized Morita-Mumford classes in;J 's (i 􀀵 0, j 􀀵 1, i + j 􀀵 2) [Ka) over the rational stable cohomology algebra of the group r g,1 •
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