Characteristic classes of foliated surface bundles with area-preserving holonomy

Details Characteristic classes of foliated surface bundles with area-preserving holonomy Characteristic classes of foliated surface bundles with area-preserving holonomy

2004-09-13

arxiv.org/abs/math/0409214v2

Journal of Differential Geometry 75 (2007), 273--302

Mathematics

Symplectic Geometry

minor improvements to the exposition; to appear in Journal of Differential Geometry

Scientific paper

Making use of the extended flux homomorphism on the group of symplectomorphisms of a closed oriented surface of genus at least 2, we introduce new characteristic classes of foliated surface bundles with symplectic, equivalently area-preserving, total holonomy. These characteristic classes are stable with respect to the genus and we show that they are highly non-trivial. We also prove that the second homology of the group of Hamiltonian symplectomorphisms equipped with the discrete topology is very large.

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