On the Quantum Cohomology of Fano Toric Manifolds and the Intersection Cohomology of Singular Symplectic Quotients

Ho, Jeffrey

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Description

Title

On the Quantum Cohomology of Fano Toric Manifolds and the Intersection Cohomology of Singular Symplectic Quotients

Author(s)

Ho, Jeffrey

Issue Date

1999

Doctoral Committee Chair(s)

Richard Bishop

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

Mathematics

Language

eng

Abstract

The second result computes the intersection cohomology of the singular symplectic reduced spaces. Let M be a closed symplectic manifold with a Hamiltonian S1-action defined on it and mu is the moment map. If 0 is a singular value of mu, the reduced space mu-1(0)/S1 is, in general, no longer an orbifold but contains singularities. We show that there is a surjective map from the equivariant cohomology of M to the intersection cohomology of mu-1(0)/ S1. This result can be considered as a symplectic generalization of the Beilinson-Bernstein-Deligne-Gabor decomposition theorem for singular algebraic varieties. Using this surjectivity result and the localization technique, we can relate the pairings of the intersection cohomology classes to the equivariant cohomology classes in M. We show that a theorem of Kalkman has a direct generalization in the singular setting.

Graduation Semester

1999

Type of Resource

text

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http://hdl.handle.net/2142/86983

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