The Intersection Cohomology of Singular Symplectic Quotients
نویسنده
چکیده
We give a general procedure for the calculation of the intersection Poincaré polynomial of the symplectic quotient M/K, of a symplectic manifold M by a hamiltonian group action of a compact Lie group K. The procedure mirrors that used by Kirwan for the calculation of the intersection Poincaré polynomial of a geometric invariant theory quotient of a nonsingular complex projective variety. That is, we proceed inductively on a partial desingularisation of the quotient. This allows us to reduce to the nonsingular case which is calculable (by using Morse theory on the norm square of the moment map). As in the algebraic setting there is a surjection H∗ K (M) −→ IH∗(M/K) from the equivariant cohomology of M to the intersection cohomology of the quotient.
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