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• W4297665278 abstract "This work is NOT to be used as reference. First, because as C.F.~Bodigheimer and M.~Korkmaz pointed to us the computation of the $mathbf{Z}_2$ factor that remained undecided in M.~Korkmaz and A. Stipsicz, {em The second homology groups of mapping class groups of orientable surfaces.} Math. Proc. Camb. Phil. Soc., was shown to exist by Skasai, see hi Theorem 4.9 and Corollary 4.10 in {em Lagrangian mapping class groups from a group homological point of view.} Algebr. Geom. Topol. 12 (2012), no. 1, 267--291. Second, because one could obtain this result by gathering old results in the literature, first by noticing as Korkmaz kindly reminded me, that D.~Johnson, in emph{Homeomorphisms of a surface which act trivially on homology} Porc. AMS Volume 75, Number 1, 1979. proved that the quotient of the Torelli group $mathcal{T}_g/[mathcal{T}_g,mathcal{M}_g]$ is trivial for $ggeq 3$, the five term exact sequence then implies that the $mathbf{Z}_2$ factor in Stein's computation of $H_2(Sp(6,mathbf{Z});mathbf{Z}) = mathbf{Z}oplusmathbf{Z}_2$ (see his {em The Schur Multipliers of $Sp_6(mathbf{Z}), Spin_8(mathbf{Z}), Spin_7(mathbf{Z}),$ and $F_4(mathbf{Z})$.} Math. Ann. 215 (1975), 173--193. ), detects the undecided $mathbf{Z}_2$ factor in $H_2(mathbf{M}_3;mathbf{Z})$." @default.
• W4297665278 created "2022-09-30" @default.
• W4297665278 creator A5022056632 @default.
• W4297665278 date "2013-11-22" @default.
• W4297665278 modified "2023-09-26" @default.
• W4297665278 title "The 2-torsion in the second homology of the genus $3$ mapping class group" @default.
• W4297665278 doi "https://doi.org/10.48550/arxiv.1311.5705" @default.
• W4297665278 hasPublicationYear "2013" @default.
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