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A Generalization of the Morita-Mumford Classes to Extended Mapping Class Groups for Surfaces
| 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 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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
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Submitter: 数学紀要登録作業用
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