Gromov-Witten invariants and pseudo symplectic capacities |
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Authors: | Guangcun Lu |
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Institution: | (1) Department of Mathematics, Beijing Normal University, 100875 Beijing, P.R. China |
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Abstract: | We introduce the concept of pseudo symplectic capacities which is a mild generalization of that of symplectic capacities.
As a generalization of the Hofer-Zehnder capacity we construct a Hofer-Zehnder type pseudo symplectic capacity and estimate
it in terms of Gromov-Witten invariants. The (pseudo) symplectic capacities of Grassmannians and some product symplectic manifolds
are computed. As applications we first derive some general nonsqueezing theorems that generalize and unite many previous versions
then prove the Weinstein conjecture for cotangent bundles over a large class of symplectic uniruled manifolds (including the
uniruled manifolds in algebraic geometry) and also show that any closed symplectic submanifold of codimension two in any symplectic
manifold has a small neighborhood whose Hofer-Zehnder capacity is less than a given positive number. Finally, we give two
results on symplectic packings in Grassmannians and on Seshadri constants.
Partially supported by the NNSF 10371007 of China and the Program for New Century Excellent Talents of the Education Ministry
of China. |
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