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Original Articles

Some computations of stable twisted homology for mapping class groups

Pages 2467-2491 | Received 27 Nov 2018, Accepted 31 Dec 2019, Published online: 26 Jan 2020

References

  • Arnold, V. I. (1969). The cohomology ring of the colored braid group. In: Givental, A. B., Khesin, B., Varchenko, A. N., Vassiliev, V. A., Viro, O. Y., eds. Vladimir I. Arnold-Collected Works. New York, NY: Springer, pp. 183–186.
  • Birman, J. S. (1974). Braids, Links, and Mapping Class Groups. Princeton, NJ/Tokyo, Japan; Princeton University Press/University of Tokyo Press. Annals of Mathematics Studies, No. 82.
  • Bödigheimer, C.-F., Tillmann, U. (2001). Stripping and splitting decorated mapping class groups. In: Cohomological Methods in Homotopy Theory (Bellaterra, 1998), Volume 196 of Progr. Math. Basel, Switzerland: Birkhäuser, pp. 47–57.
  • Boldsen, S. K. (2012). Improved homological stability for the mapping class group with integral or twisted coefficients. Math. Z. 270(1/2):297–329. DOI: 10.1007/s00209-010-0798-y.
  • Brown, K. S. (2012). Cohomology of Groups, Vol. 87. Berlin, Germany: Springer Science & Business Media.
  • Cerf, J. (1961). Topologie de certains espaces de plongements. Bull. Soc. Math. France 89: 227–380. DOI: 10.24033/bsmf.1567.
  • Church, T., Ellenberg, J. S., Farb, B. (2015). FI-modules and stability for representations of symmetric groups. Duke Math. J. 164(9):1833–1910. DOI: 10.1215/00127094-3120274.
  • Cohen, R. L., Madsen, I. (2009). Surfaces in a background space and the homology of mapping class groups. In: Algebraic Geometry—Seattle 2005. Part 1, Volume 80 of Proc. Sympos. Pure Math. Providence, RI: American Mathematical Society, pp. 43–76.
  • Djament, A., Vespa, C. (2010). Sur l’homologie des groupes orthogonaux et symplectiques à coefficients tordus. Ann. Sci. École Norm. Sup. 43(3):395–459. DOI: 10.24033/asens.2125.
  • Djament, A., Vespa, C. (2015). Sur l’homologie des groupes d’automorphismes des groupes libres à coefficients polynomiaux. Comment. Math. Helv. 90(1):33–58. DOI: 10.4171/CMH/345.
  • Djament, A., Vespa, C. (2019). Foncteurs faiblement polynomiaux. Int. Math. Res. Not. IMRN 2019(2):321–391. DOI: 10.1093/imrn/rnx099.
  • Franjou, V., Pirashvili, T. (2003). Stable K-theory is bifunctor homology (after A. Scorichenko). In: Rational Representations, the Steenrod Algebra and Functor Homology, Volume 16 of Panor. Synthèses. Paris, France: Société mathématique de France, pp. 107–126.
  • Galatius, S. (2011). Stable homology of automorphism groups of free groups. Ann. Math. 173(2):705–768.
  • Gandini, G., Wahl, N. (2016). Homological stability for automorphism groups of RAAGs. Algebr. Geom. Topol. 16(4):2421–2441. DOI: 10.2140/agt.2016.16.2421.
  • Godement, R. (1958). Topologie algébrique et théorie des faisceaux. Actualités Sci. Ind. No. 1252. Publ. Math. Univ. Strasbourg. No. 13. Paris, France: Hermann.
  • Gramain, A. (1973). Le type d’homotopie du groupe des difféomorphismes d’une surface compacte. In: Annales scientifiques de l’École Normale Supérieure, Vol. 6. Amsterdam, Netherlands: Elsevier, pp. 53–66. DOI: 10.24033/asens.1242.
  • Grayson, D. (1976). Higher algebraic K-theory: II (after Daniel Quillen). In: Algebraic K-theory. Lectures Notes in Math., Vol. 551. Berlin, Germany: Springer, pp. 217–240.
  • Harer, J. (1991). The third homology group of the moduli space of curves. Duke Math. J. 63(1):25–55. DOI: 10.1215/S0012-7094-91-06302-7.
  • Harer, J. L. (1985). Stability of the homology of the mapping class groups of orientable surfaces. Ann. Math. 121(2):215–249. DOI: 10.2307/1971172.
  • Hatcher, A. (2002). Algebraic Topology. Cambridge, UK: Cambridge University Press, pp. 606–609.
  • Hatcher, A., Wahl, N. (2005). Stabilization for the automorphisms of free groups with boundaries. Geom. Topol. 9(3):1295–1336. DOI: 10.2140/gt.2005.9.1295.
  • Hatcher, A., Wahl, N. (2010). Stabilization for mapping class groups of 3-manifolds. Duke Math. J. 155(2):205–269. DOI: 10.1215/00127094-2010-055.
  • Jensen, C. A. (2004). Homology of holomorphs of free groups. J. Algebra 271(1):281–294. DOI: 10.1016/j.jalgebra.2003.08.019.
  • Jensen, C. A., Wahl, N. (2004). Automorphisms of free groups with boundaries. Algebr. Geom. Topol. 4(1):543–569. DOI: 10.2140/agt.2004.4.543.
  • Kawazumi, N. (2008). On the stable cohomology algebra of extended mapping class groups for surfaces. In: Groups of Diffeomorphisms, Volume 52 of Adv. Stud. Pure Math. Tokyo, Japan: Math. Soc. Japan, pp. 383–400.
  • Lane, S. M. (2013). Categories for the Working Mathematician, Vol. 5. Berlin, Germany: Springer Science & Business Media.
  • Madsen, I., Weiss, M. (2007). The stable moduli space of Riemann surfaces: Mumford’s conjecture. Ann. Math. 165(3):843–941. DOI: 10.4007/annals.2007.165.843.
  • Randal-Williams, O., Wahl, N. (2017). Homological stability for automorphism groups. Adv. Math. 318: 534–626. DOI: 10.1016/j.aim.2017.07.022.
  • Soulié, A. (2018). The generalized Long-Moody functors. arXiv:1709.04278.
  • Soulié, A. (2019). The long–moody construction and polynomial functors. Annales de l’Institut Fourier 69(4):1799–1856. DOI: 10.5802/aif.3282.
  • Vogtmann, K. (2015). GL(n,Z), Out(Fn) and everything in between: automorphism groups of RAAGs. In: Groups St Andrews 2013, Volume 422 of London Math. Soc. Lecture Note Ser. Cambridge, UK: Cambridge University Press, pp. 105–127.
  • Weibel, C. A. (1994). An Introduction to Homological Algebra, Volume 38 of Cambridge Studies in Advanced Mathematics. Cambridge, UK: Cambridge University Press.

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