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Intersection Cohomology of Symplectic Quotients by Circle Actions
Author(s) -
Kiem Young-Hoon,
Woolf Jonathan
Publication year - 2005
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610704006118
Subject(s) - mathematics , intersection homology , equivariant cohomology , symplectic geometry , moment map , pure mathematics , cohomology , quotient , sheaf cohomology , sheaf , equivariant map
Let T = U (1) and M be a Hamiltonian T ‐space with proper moment map μ : M → R. When 0 is not a regular value of μ, the symplectic quotient X = μ −1 (0)/ T is a singular stratified space. A description is provided of the middle perversity intersection cohomology of X as a subspace of the equivariant cohomologyH T * ( μ − 1 ( 0 ) ) . The approach is sheaf theoretic.