2024-03-29T07:22:58Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/690622022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116On the stable cohomology algebra of extended mapping class groups for surfacesKawazumi, N.open access410Let :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 •Department of Mathematics, Hokkaido University1995-10-01engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83458http://hdl.handle.net/2115/6906210.14943/83458Hokkaido University Preprint Series in Mathematics311113https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69062/1/pre311.pdfapplication/pdf819.71 KB1995-10-01