Floer theory for negative line bundles via Gromov-Witten invariants

Details Floer theory for negative line bundles via Gromov-Witten invariants Floer theory for negative line bundles via Gromov-Witten invariants

2011-06-20

arxiv.org/abs/1106.3975v2

Mathematics

Symplectic Geometry

50 pages; version 2: short proof of Kodaira vanishing, clarified proof of r(1)=c_1(L), improved exposition

Scientific paper

Let M be the total space of a negative line bundle over a closed symplectic manifold. We prove that the quotient of quantum cohomology by the kernel of a power of quantum cup product by the first Chern class of the line bundle is isomorphic to symplectic cohomology. We also prove this for negative vector bundles and the top Chern class. We explicitly calculate the symplectic and quantum cohomologies of O(-n) over P^m. For n=1, M is the blow-up of C^{m+1} at the origin and symplectic cohomology has rank m. The symplectic cohomology vanishes if and only if the first Chern class of the line bundle is nilpotent in quantum cohomology. We prove a Kodaira vanishing theorem and a Serre vanishing theorem for symplectic cohomology. In general, we construct a representation of \pi_1(Ham(X,\omega)) on the symplectic cohomology of symplectic manifolds X conical at infinity.

Affiliated with

Also associated with

No associations

Rating

Floer theory for negative line bundles via Gromov-Witten invariants does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Floer theory for negative line bundles via Gromov-Witten invariants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Floer theory for negative line bundles via Gromov-Witten invariants will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-256407