Fibered Symplectic Cohomology and the Leray-serre Spectral Sequence
نویسنده
چکیده
We define Symplectic cohomology groups FH∗ [a,b] (E), −∞ ≤ a < b ≤ ∞ for a class of symplectic fibrations F →֒ E −→ B with closed symplectic base and convex at infinity fiber. The crucial geometric assumption on the fibration is a negativity property reminiscent of negative curvature in complex vector bundles. When B is symplectically aspherical we construct a spectral sequence of Leray-Serre type converging to FH∗ [a,b] (E), and we use it to prove new cases of the Weinstein conjecture.
منابع مشابه
Fibered Symplectic Homology and the Leray-serre Spectral Sequence
We define Floer (or Symplectic) cohomology groups FH ]a, b] (E), −∞ ≤ a < b ≤ ∞ for a class of monotone symplectic fibrations F →֒ E −→ B with closed symplectic base and convex at infinity fiber. The crucial geometric assumption on the fibration is a negativity property reminiscent of negative curvature in complex vector bundles. Our construction is a fibered extension of a construction of Viter...
متن کاملControlled K-theory I: Basic theory
This paper provides a full controlled version of algebraic K-theory. This includes a rich array of assembly maps; the controlled assembly isomorphism theorem identifying the controlled group with homology; and the stability theorem describing the behavior of the inverse limit as the control parameter goes to 0. There is a careful treatment of spectral cosheaf homology and related tools, includi...
متن کاملSheaf Cohomology, and the Heterotic Standard Model
Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the elliptically fibered covering space. The cohomology groups of the vector bundle, which yield the low energy spectrum, are computed using the Leray spectral sequen...
متن کاملVector Bundle Extensions, Sheaf Cohomology, and the Heterotic Standard Model
Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the elliptically fibered covering space. The cohomology groups of the vector bundle, which yield the low energy spectrum, are computed using the Leray spectral sequen...
متن کاملTopic Proposal The Cohomology of Configuration Space and Representation Stability
The theory of the configuration space of a manifold provides illustrative examples of a number of topological phenomena. We begin with a discussion of the configuration space of the complex plane, and give a classical description of the braid and pure braid groups. We next give an alternative interpretation of the braid groups as mapping classes of punctured disks, an interpretation which provi...
متن کامل