Continuous cohomology of the group of volume-preserving and symplectic diffeomorphisms, measurable transfer and higher asymptotic cycles

Selecta Mathematica, New Series

Volumn 5, Issue 1, 1999, Pages 181-198

  Reznikov, Alexander ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Continuous cohomology; Symplectomorphism groups

Indexed keywords

EID: 35148815501     PISSN: 10221824     EISSN: 14209020     Source Type: Journal    
DOI: 10.1007/s000290050046     Document Type: Article

References (25)

1. [A] V. Arnold, a manuscript in Russian (1965).
2. [B] A. Borel. Stable real cohomology of arithmetic groups. Ann. Sci. Ec. Norm. Super. 7 (1974), 235-272.
3. [BCG] G. Besson, G. Courtois and S. Gallot. In preparation.
4. [Bo] R. Bott. On the characteristic classes of groups of diffeomorphisms. Enseignement Math. (2) 23 (1977), 209-220.
5. [BG] J. Barge and E. Ghys. Cocycles d'Euler et de Maslov. Math. Ann. 294 (1992), 235-265.
6. [BGo] R. Brooks and W. Goldman. Volumes in Seifert space. Duke Math. J. 51 (1984), 529-545.
7. [Br] R. Brooks. Volumes and characteristic classes of foliations. Topology 18 (1979), 295-304.
8. [D] J.L. Dupont. Simplicial DeRham cohomology and characteristic classes of flat bundles. Topology 18 (1979), 295-304.
9. [FJ] F. Farrell and L. Jones. Isomorphism conjectures in Algebraic K-theory. Journ. AMS 6 (1993), 249-297.
10. [Go] A. Goncharov. In preparation.
11. [Gol1] W. Goldman. Berkeley Thesis (1980).
12. [Gol2] W. Goldman. Invariant functions on Lie groups and Hamiltonian flows on surface grou representations. Inv. Math 85 (1986), 263-302.
13. [Gr] M. Gromov. Pseudoholomorphic curves in symplectic manifolds. Inv. Math. 82 (1985), 307-347.
14. [Gr2] M. Gromov. Volume and bounded cohomology. Publ. Math. IHES 56, 5-99.
15. [Gu] A. Guichardet. Cohomologie des Groupes Topologiques et des Algébres de Lie. Cedic, 1980.
16. [Ha] A. Hatcher. A proof of a Smale's conjecture. Ann. of Math. 117 (1983), 553-607.
17. [I] N. Ivanov. Soviet Math. Dokl. 20 (1979), 47-50.
18. [M] Y. Mitsumatsu. Bounded cohomology and -4-homology of surfaces. Topology 23 (1984), 465-471.
19. [NS] M.S. Narasimhan,C.S. Seshadri. Stable and unitary bundles on a compact Riemann surface. Annals of Math. 82 (1965), 540-564.
20. [Rel] A. Reznikov. Twistor varieties, symplectic reduction and universal Jacobians. Preprint MPI, August, 1996.
21. [Re2] A. Reznikov. Characteristic classes in symplectic topology. Selecta math. New ser. 3 (1997), 401-442.
22. [Re3] A. Reznikov. Rationality of secondary classes. J. Diff. Geom. 43 (1996), 674-692.
23. 1, submitted.
24. [Sch] W. Schwartzmann. Asymptotic cycles. Annals of Mathematics 66 (1957), 270-284.
25. [Th] W. Thurston. The Geometry and Topology of 3-Manifolds.