Some canonical cohomology classes on groups of volume preserving diffeomorphisms

Author:
Dusa McDuff

Journal:
Trans. Amer. Math. Soc. **275** (1983), 345-356

MSC:
Primary 58H10; Secondary 57R50, 57T99, 58D05

DOI:
https://doi.org/10.1090/S0002-9947-1983-0678355-7

MathSciNet review:
678355

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Abstract: We discuss some canonical cohomology classes on the space , where is the identity component of the group of compactly supported diffeomorphisms of the manifold which preserve the volume form . We first look at some classes , which are defined for all , and show that the top class is nonzero for odd, and is zero for even. When for , the classes all vanish and a secondary class may be defined. This is trivially zero when is odd, and is twice the Calabi invariant for symplectic manifolds when . We prove that when is even by showing that it is one of a set of nonzero classes which were defined by Hurder in [**7**].

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1983-0678355-7

Article copyright:
© Copyright 1983
American Mathematical Society