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A Generalization of the Morita-Mumford Classes to Extended Mapping Class Groups for Surfaces

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83439

Title: A Generalization of the Morita-Mumford Classes to Extended Mapping Class Groups for Surfaces
Authors: Kawazumi, N. Browse this author
Issue Date: 1-Apr-1995
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 292
Start Page: 1
End Page: 11
Abstract: Let :E9,1 be an orientable compact surface of genus g with 1 boundary component, and r g,1 the mapping class group of :E9,1. We define a bigraded series of cohomology classes mi,j E H2i+i-2 (f9,1 ;/\/ H1 (:E9,1;Z)), 2i+j-2 ;:=: 1, i,j ;:=: 0. When j = 0, the class mi+1 ,o is the i-th Morita-Mumford class [Mo][Mu]. It is proved that Hr (r9,1;/\8 H1 (:E9,1;Q)) is generated by m;,j's for the case r + s = 2 and the case g ;:=: 5 and (r, s) = (1, 3). Especially the Johnson homomorphism extended to the whole mapping class group by Morita [Mo3] has an implicit representation by the classes mo,3 and mo,2m1,1 over Q.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69043
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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