Characteristic classes of foliated surface bundles with area-preserving holonomy
Symplectic Geometry
2007-05-23 v2 Algebraic Topology
Geometric Topology
Abstract
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.
Cite
@article{arxiv.math/0409214,
title = {Characteristic classes of foliated surface bundles with area-preserving holonomy},
author = {D. Kotschick and S. Morita},
journal= {arXiv preprint arXiv:math/0409214},
year = {2007}
}
Comments
minor improvements to the exposition; to appear in Journal of Differential Geometry