2023-04-01T17:22:46Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/690432022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116A Generalization of the Morita-Mumford Classes to Extended Mapping Class Groups for SurfacesKawazumi, N.open access410Let :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.Department of Mathematics, Hokkaido University1995-04-01engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83439http://hdl.handle.net/2115/6904310.14943/83439Hokkaido University Preprint Series in Mathematics292111https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69043/1/pre292.pdfapplication/pdf569.61 KB1995-04-01