Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T18:26:59.089Z Has data issue: false hasContentIssue false

On the Cohomology of Classifying Spaces of Groups of Homeomorphisms

Published online by Cambridge University Press:  10 April 2014

Jarek Kȩdra*
Affiliation:
School of Natural and Computing Sciences, University of Aberdeen, King's College, Aberdeen AB24 3FX, UK, (xlink:href="[email protected]">[email protected]) Institute of Mathematics, University of Szczecin, ul. Wielkopolska 15, 70-451 Szczecin, Poland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let M be a closed simply connected 2n-dimensional manifold. The paper is concerned with the cohomology of classifying spaces of connected groups of homeomorphisms of M.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2014 

References

1.Blanchard, A., Sur les variétés analytiques complexes, Annales Scient. Ec. Norm. Sup. 73 (1956), 157202.Google Scholar
2.Bott, R., An application of the Morse theory to the topology of Lie-groups, Bull. Soc. Math. France 84 (1956), 251281.CrossRefGoogle Scholar
3.Gal, Ś. R., Kȩdra, J. and Tralle, A., On algebraic independence of Hamiltonian characteristic classes, J. Symp. Geom. 9(1) (2011), 1117.CrossRefGoogle Scholar
4.Griffiths, P. and Harris, J., Principles of algebraic geometry, Wiley Classics Library, Volume 52 (Wiley, 1994).Google Scholar
5.Guillemin, V., Lerman, E. and Sternberg, S., Symplectic fibrations and multiplicity diagrams (Cambridge University Press, 1996).Google Scholar
6.Hatcher, A., Algebraic topology (Cambridge University Press, 2002).Google Scholar
7.Januszkiewicz, T. and Kedra, J., Characteristic classes of smooth fibrations, eprint (arXiv:math/0209288, 2002).Google Scholar
8.Kedra, J. and Mcduff, D., Homotopy properties of Hamiltonian group actions, Geom. Topol. 9 (2005), 121162.Google Scholar
9.Kedra, J., Tralle, A. and Woike, A., On nondegenerate coupling forms, J. Geom. Phys. 61(2) (2011), 462475.Google Scholar
10.Lalonde, F. and Mcduff, D., Symplectic structures on fiber bundles, Topology 42(2) (2003), 309347.Google Scholar
11.Luke, G. L., Representation theory of Lie groups, London Mathematical Society Lecture Note Series, Volume 34 (Cambridge University Press, 1979).Google Scholar
12.Pedroza, A., Seidel's representation on the Hamiltonian group of a Cartesian product, Int. Math. Res. Not. 2008 (2008), 10.1093/imrn/rnn049.Google Scholar
13.Reznikov, A. G., Characteristic classes in symplectic topology, Selecta Math. 3(4) (1997), 601642.Google Scholar
14.Seidel, P., On the group of symplectic automorphisms of ℂPm × ℂPn, in Northern California symplectic geometry seminar, American Mathematical Society Translations, Volume 196, pp. 237250 (American Mathematical Society, Providence, RI, 1999).Google Scholar