The homology of surface diffeomorphism groups and a question of Morita
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Abstract:
We answer a question posed by Morita concerning the non-trivial- ity of certain secondary characteristic classes for surface bundles. In doing so we are naturally led to show that a form of Harer stability holds for surface diffeomorphism groups in homology of small degree.References
- Raoul Bott, Lectures on characteristic classes and foliations, Lectures on algebraic and differential topology (Second Latin American School in Math., Mexico City, 1971) Lecture Notes in Math., Vol. 279, Springer, Berlin, 1972, pp. 1–94. Notes by Lawrence Conlon, with two appendices by J. Stasheff. MR 0362335
- C. J. Earle and A. Schatz, Teichmüller theory for surfaces with boundary, J. Differential Geometry 4 (1970), 169–185. MR 277000, DOI 10.4310/jdg/1214429381
- S. Haller, Perfectness and simplicity of certain groups of diffeomorphisms, Ph.D. Thesis, University of Vienna, 1998. Available at: http://www.mat.univie.ac.at/~stefan/files/diss.pdf.
- N. Ivanov, Mapping Class Groups, 1998 (electronic). Available at: http://www.mth.msu.edu/~ivanov/indexmath.html.
- D. Kotschick and S. Morita, Signatures of foliated surface bundles and the symplectomorphism groups of surfaces, Topology 44 (2005), no. 1, 131–149. MR 2104005, DOI 10.1016/j.top.2004.05.002
- J. Mather, On the homology of Haefliger’s classifying space, course given at Varenna, 1976, CIME Differential Topology, Leguore editore, Napoli, 1979, 73–116.
- Shigeyuki Morita, Cohomological structure of the mapping class group and beyond, Problems on mapping class groups and related topics, Proc. Sympos. Pure Math., vol. 74, Amer. Math. Soc., Providence, RI, 2006, pp. 329–354. MR 2264550, DOI 10.1090/pspum/074/2264550
- Ole Hjorth Rasmussen, Continuous variation of foliations in codimension two, Topology 19 (1980), no. 4, 335–349. MR 584559, DOI 10.1016/0040-9383(80)90018-X
- William Thurston, Foliations and groups of diffeomorphisms, Bull. Amer. Math. Soc. 80 (1974), 304–307. MR 339267, DOI 10.1090/S0002-9904-1974-13475-0
- T. Tsuboi, Classifying space for groupoid structures, 2001. Conference talk notes, available at www.foliations.org/surveys/Rio2001_BGamma.pdf.
Additional Information
- Jonathan Bowden
- Affiliation: Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstr. 39, 80333 München, Germany
- Address at time of publication: Mathematisches Institut, Universität Augsburg, Universitätsstr. 14, 86159 Augsburg, Germany
- MR Author ID: 873123
- Email: jonathan.bowden@mathematik.uni-muenchen.de
- Received by editor(s): February 18, 2011
- Published electronically: November 4, 2011
- Communicated by: Daniel Ruberman
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 2543-2549
- MSC (2010): Primary 57R30, 57R50; Secondary 57R32
- DOI: https://doi.org/10.1090/S0002-9939-2011-11259-0
- MathSciNet review: 2898716