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The homology of surface diffeomorphism groups and a question of Morita
Author:
Jonathan Bowden
Journal:
Proc. Amer. Math. Soc. 140 (2012), 2543-2549
MSC (2010):
Primary 57R30, 57R50; Secondary 57R32
Posted:
November 4, 2011
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Additional Information
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
- [Bott]
Raoul
Bott, Lectures on characteristic classes and foliations,
Lectures on algebraic and differential topology (Second Latin American
School in Math., Mexico City, 1971), Springer, Berlin, 1972,
pp. 1–94. Lecture Notes in Math., Vol. 279. Notes by Lawrence
Conlon, with two appendices by J. Stasheff. MR 0362335
(50 #14777)
- [ES]
C.
J. Earle and A.
Schatz, Teichmüller theory for surfaces with boundary, J.
Differential Geometry 4 (1970), 169–185. MR 0277000
(43 #2737b)
- [Hal]
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.
- [Iva]
N. Ivanov, Mapping Class Groups, 1998 (electronic). Available at: http://www.mth.msu.edu/~ivanov/indexmath.html.
- [KM]
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
(2005k:57050), http://dx.doi.org/10.1016/j.top.2004.05.002
- [Math]
J. Mather, On the homology of Haefliger's classifying space, course given at Varenna, 1976, CIME Differential Topology, Leguore editore, Napoli, 1979, 73-116.
- [Mor]
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
(2007j:20079)
- [Ras]
Ole
Hjorth Rasmussen, Continuous variation of foliations in codimension
two, Topology 19 (1980), no. 4, 335–349.
MR 584559
(82i:57027), http://dx.doi.org/10.1016/0040-9383(80)90018-X
- [Th]
William
Thurston, Foliations and groups of diffeomorphisms, Bull.
Amer. Math. Soc. 80 (1974), 304–307. MR 0339267
(49 #4027)
- [Tsu]
T. Tsuboi, Classifying space for groupoid structures, 2001. Conference talk notes, available at www.foliations.org/surveys/Rio2001_BGamma.pdf.
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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
Email:
jonathan.bowden@mathematik.uni-muenchen.de
DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-11259-0
PII:
S 0002-9939(2011)11259-0
Received by editor(s):
February 18, 2011
Posted:
November 4, 2011
Communicated by:
Daniel Ruberman
Article copyright:
© Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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