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Journal of the London Mathematical Society 2005 71(2):531-544; doi:10.1112/S0024610704006118
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© The London Mathematical Society

Intersection Cohomology of Symplectic Quotients by Circle Actions

Young-Hoon Kiem and Jonathan Woolf

Department of Mathematics, Seoul National University Seoul 151-747, Korea kiem{at}math.snu.ac.kr
Christ's College, University of Cambridge Cambridge, CB2 3BU, United Kingdom jw301{at}cam.ac.uk

Received 2 December 2003. Revision received 30 March 2004.

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 cohomology Formula. The approach is sheaf theoretic.


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