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Characteristic classes of foliated surface bundles with area-preserving holonomy

D. Kotschick Ludwig-Maximilians-Universit¨at M¨unchen S. Morita University of Tokyo

Differential Geometry mathscidoc:1609.10007

Journal of Differential Geometry, 75, 273-302, 2007
Making use of the extended flux homomorphism defined in [13] on the group Symp§g of symplectomorphisms of a closed ori- ented surface §g of genus g ≥ 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 g and we show that they are highly non- trivial. We also prove that the second homology of the group Ham§g of Hamiltonian symplectomorphisms of §g, equipped with the discrete topology, is very large for all g ≥ 2.
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@inproceedings{d.2007characteristic,
  title={CHARACTERISTIC CLASSES OF FOLIATED SURFACE BUNDLES WITH AREA-PRESERVING HOLONOMY},
  author={D. Kotschick, and S. Morita},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160908192900209979664},
  booktitle={Journal of Differential Geometry},
  volume={75},
  pages={273-302},
  year={2007},
}
D. Kotschick, and S. Morita. CHARACTERISTIC CLASSES OF FOLIATED SURFACE BUNDLES WITH AREA-PRESERVING HOLONOMY. 2007. Vol. 75. In Journal of Differential Geometry. pp.273-302. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160908192900209979664.
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