Homological stability of non-orientable mapping class groups with marked points
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- by Elizabeth Hanbury
- Proc. Amer. Math. Soc. 137 (2009), 385-392
- DOI: https://doi.org/10.1090/S0002-9939-08-09519-1
- Published electronically: August 18, 2008
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Abstract:
Wahl recently proved that the homology of the non-orientable mapping class group stabilizes as the genus increases. In this short paper we analyse the situation where the underlying non-orientable surfaces have marked points.References
- Stanislaw Betley, Twisted homology of symmetric groups, Proc. Amer. Math. Soc. 130 (2002), no. 12, 3439–3445. MR 1918818, DOI 10.1090/S0002-9939-02-06763-1
- Carl-Friedrich Bödigheimer and Ulrike Tillmann, Stripping and splitting decorated mapping class groups, Cohomological methods in homotopy theory (Bellaterra, 1998) Progr. Math., vol. 196, Birkhäuser, Basel, 2001, pp. 47–57. MR 1851247
- Clifford J. Earle and James Eells, A fibre bundle description of Teichmüller theory, J. Differential Geometry 3 (1969), 19–43. MR 276999
- Clifford J. Earle and James Eells, A fibre bundle description of Teichmüller theory, J. Differential Geometry 3 (1969), 19–43. MR 276999
- Samuel Eilenberg and Saunders Mac Lane, On the groups $H(\Pi ,n)$. II. Methods of computation, Ann. of Math. (2) 60 (1954), 49–139. MR 65162, DOI 10.2307/1969702
- John L. Harer, Stability of the homology of the mapping class groups of orientable surfaces, Ann. of Math. (2) 121 (1985), no. 2, 215–249. MR 786348, DOI 10.2307/1971172
- A. Hatcher and N. Wahl. Stabilization for mapping class groups of $3$-manifolds, 2007. arXiv:math.GT/0709.2173.
- Nikolai V. Ivanov, On the homology stability for Teichmüller modular groups: closed surfaces and twisted coefficients, 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. 149–194. MR 1234264, DOI 10.1090/conm/150/01290
- Nathalie Wahl, Homological stability for the mapping class groups of non-orientable surfaces, Invent. Math. 171 (2008), no. 2, 389–424. MR 2367024, DOI 10.1007/s00222-007-0085-7
Bibliographic Information
- Elizabeth Hanbury
- Affiliation: Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford, OX1 3LB
- Address at time of publication: Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543
- Email: mathe@nus.edu.sg
- Received by editor(s): June 6, 2007
- Received by editor(s) in revised form: January 17, 2008
- Published electronically: August 18, 2008
- Communicated by: Paul Goerss
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 385-392
- MSC (2000): Primary 57N05; Secondary 20F38
- DOI: https://doi.org/10.1090/S0002-9939-08-09519-1
- MathSciNet review: 2439464