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Richard Bishop Ho, Jeffrey 2015-09-28T15:20:28Z 2015-09-28T15:20:28Z 10000-01-01 1999 1999 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. Made available in DSpace on 2015-09-28T15:20:28Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9953047.pdf: 2751151 bytes, checksum: fa7105d46700e57a4e1449d68e7ed3da (MD5) Previous issue date: 1999 Embargo set by: Seth Robbins for item 88264 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 79 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1999. http://hdl.handle.net/2142/86983 (MiAaPQ)AAI9953047 eng Mathematics On the Quantum Cohomology of Fano Toric Manifolds and the Intersection Cohomology of Singular Symplectic Quotients text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.