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Topology/Geometry Seminar
Thursday, February 3, 2005
5:00-6:00pm,
122 Pond Lab (UP)
David Hurtubise
Penn State Altoona
The Seidel Element in Quantum Cohomology, Part I
Abstract: Let (M,ω) be a compact monotone symplectic manifold. Associated to every loop of Hamiltonian symplectomorphisms φt of M there is a cohomology class S( φ) called the Seidel element. In fact, the Seidel element determines a group homomorphism from the fundamental group of the group of Hamiltonian symplectomorphisms of (M,ω) to the multiplicative group of invertible elements of the quantum cohomology of M. In these talks I will first describe the results concerning compactified moduli spaces of J-holomorphic sections of locally trivial Hamiltonian fibrations needed to define the Seidel element. I will then define the Seidel element and describe some of its applications. These talks will be a survey of the results related to the Seidel element and few (if any) proofs will be included.
