A Gysin sequence for manifolds with R action
نویسنده
چکیده
We associate an exact sequence involving the cohomology groups of a pair of differential complexes to any pair (N , T ) where N is a closed connected smooth manifold and T a real nowhere vanishing smooth vector field on N that admits an invariant metric. The orbits of T need not be closed. The sequence is a natural generalization of the classical Gysin sequence (for circle bundles) in real cohomology.
منابع مشابه
ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE
A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds...
متن کاملOn the localization formula in equivariant cohomology
We give a generalization of the Atiyah–Bott–Berline–Vergne localization theorem for the equivariant cohomology of a torus action. We replace the manifold having a torus action by an equivariant map of manifolds having a compact connected Lie group action. This provides a systematic method for calculating the Gysin homomorphism in ordinary cohomology of an equivariant map. As an example, we reco...
متن کاملIntersection Cohomology of S1-actions on Pseudomanifolds
For any smooth free action of the unit circle S in a manifold M ; the Gysin sequence of M is a long exact sequence relating the DeRham cohomologies of M and its orbit space M/S. If the action is not free then M/S is not a manifold but a stratified pseudomanifold and there is a Gysin sequence relating the DeRham cohomology of M with the intersection cohomology of M/S. In this work we extend the ...
متن کامل-actions on Pseudomanifolds
For any smooth free action of the unit circle S in a manifold M ; the Gysin sequence of M is a long exact sequence relating the DeRham cohomologies of M and its orbit space M/S. If the action is not free then M/S is not a manifold but a stratified pseudomanifold and there is a Gysin sequence relating the DeRham cohomology of M with the intersection cohomology of M/S. In this work we extend the ...
متن کاملThe Gysin exact sequence for S-equivariant symplectic homology
We define S1-equivariant symplectic homology for symplectically aspherical manifolds with contact boundary, using a Floer-type construction first proposed by Viterbo. We show that it is related to the usual symplectic homology by a Gysin exact sequence. As an important ingredient of the proof, we define a parametrized version of symplectic homology, corresponding to families of Hamiltonian func...
متن کامل