Characteristic Classes of Foliated Surface Bundles with Area-preserving Holonomy
نویسنده
چکیده
Making use of the extended flux homomorphism defined in [13] on the group SympΣg of symplectomorphisms of a closed oriented surface Σg 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 HamΣg of Hamiltonian symplectomorphisms of Σg , equipped with the discrete topology, is very large for all g ≥ 2.
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