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INTERSECTION COHOMOLOGY OF SYMPLECTIC QUOTIENTS BY CIRCLE ACTIONS

Published online by Cambridge University Press:  06 April 2005

YOUNG-HOON KIEM
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-747, Koreakiem@math.snu.ac.kr
JONATHAN WOOLF
Affiliation:
Christ's College, University of Cambridge, Cambridge, CB2 3BU, United Kingdomjw301@cam.ac.uk
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Abstract

Let $T=U(1)$ and $M$ be a Hamiltonian $T$-space with proper moment map $\mu\,{:}\,M\longrightarrow \rr$. When 0 is not a regular value of $\mu$, the symplectic quotient $X=\mu^{-1}(0)/T$ is a singular stratified space. A description is provided of the middle perversity intersection cohomology of $X$ as a subspace of the equivariant cohomology $H^*_T(\mu^{-1}(0))$. The approach is sheaf theoretic.

Type
Notes and Papers
Copyright
The London Mathematical Society 2005

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