On the cohomology of Γ_{𝑝}

Xia, Yining

doi:10.1090/S0002-9947-1995-1303129-1

On the cohomology of $\Gamma _ p$
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by Yining Xia

Trans. Amer. Math. Soc. 347 (1995), 3659-3670

DOI: https://doi.org/10.1090/S0002-9947-1995-1303129-1

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Abstract:

Let ${\Gamma _g}$ denote the mapping class group of genus $g$. In this paper, we calculate $p$-torsion of Farrell cohomology ${\widehat {H}^*}({\Gamma _p})$ for any odd prime $p$.

References

D. J. Benson and F. R. Cohen, Mapping class groups of low genus and their cohomology, Mem. Amer. Math. Soc. 90 (1991), no. 443, iv+104. MR 1052554, DOI 10.1090/memo/0443
Joan S. Birman, Mapping class groups and their relationship to braid groups, Comm. Pure Appl. Math. 22 (1969), 213–238. MR 243519, DOI 10.1002/cpa.3160220206
Kenneth S. Brown, Cohomology of groups, Graduate Texts in Mathematics, vol. 87, Springer-Verlag, New York-Berlin, 1982. MR 672956, DOI 10.1007/978-1-4684-9327-6
H. H. Glover, G. Mislin, and Y. Xia, On the Farrell cohomology of mapping class groups, Invent. Math. 109 (1992), no. 3, 535–545. MR 1176203, DOI 10.1007/BF01232038
Eduard Looijenga, Cohomology of ${\scr M}_3$ and ${\scr M}^1_3$, Mapping class groups and moduli spaces of Riemann surfaces (Göttingen, 1991/Seattle, WA, 1991) Contemp. Math., vol. 150, Amer. Math. Soc., Providence, RI, 1993, pp. 205–228. MR 1234266, DOI 10.1090/conm/150/01292
C. Maclachlan and W. J. Harvey, On mapping-class groups and Teichmüller spaces. 4, Proc. London Math. Soc. (3) 30 (1975), no. part, 496–512. MR 374414, DOI 10.1112/plms/s3-30.4.496
Yining Xia, The $p$-torsion of the Farrell-Tate cohomology of the mapping class group $\Gamma _{(p-1)/2}$, Topology ’90 (Columbus, OH, 1990) Ohio State Univ. Math. Res. Inst. Publ., vol. 1, de Gruyter, Berlin, 1992, pp. 391–398. MR 1184423
Yining Xia, The $p$-torsion of the Farrell-Tate cohomology of the mapping class group $\Gamma _{p-1}$, J. Pure Appl. Algebra 78 (1992), no. 3, 319–334. MR 1163284, DOI 10.1016/0022-4049(92)90114-U