Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9516310 | Topology | 2005 | 19 Pages |
Abstract
For any closed oriented surface Σg of genus g⩾3, we prove the existence of foliatedΣg-bundles over surfaces such that the signatures of the total spaces are non-zero. We can arrange that the total holonomy of the horizontal foliations preserve a prescribed symplectic form Ï on the fiber. We relate the cohomology class represented by the transverse symplectic form to a crossed homomorphism Flux:SympΣgâH1(Σg;R) which is an extension of the flux homomorphism Flux:Symp0ΣgâH1(Σg;R) from the identity component Symp0Σg to the whole group SympΣg of symplectomorphisms of Σg with respect to the symplectic form Ï.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
D. Kotschick, S. Morita,