The cohomology rings of abelian symplectic quotients

Details The cohomology rings of abelian symplectic quotients The cohomology rings of abelian symplectic quotients

1998-07-30

arxiv.org/abs/math/9807173v1

The cohomology rings of symplectic quotients. Communications in Analysis and Geometry 11, 751-774 (2003) (Includes the case of

Mathematics

Differential Geometry

Scientific paper

Let $M$ be a symplectic manifold, equipped with a Hamiltonian action of a torus $T$. We give an explicit formula for the rational cohomology ring of the symplectic quotient $M//T$ in terms of the cohomology ring of $M$ and fixed point data. Under some restrictions, our formulas apply to integral cohomology. In certain cases these methods enable us to show that the cohomology of the reduced space is torsion-free.

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