English

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.

Keywords

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

R2 v1 2026-07-22T17:09:43.397Z