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# Equivariant Cohomology of $S^{1}$-Actions on $4$-Manifolds

Published:2007-09-01
Printed: Sep 2007
• Leonor Godinho
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## Abstract

Let $M$ be a symplectic $4$-dimensional manifold equipped with a Hamiltonian circle action with isolated fixed points. We describe a method for computing its integral equivariant cohomology in terms of fixed point data. We give some examples of these computations.
 MSC Classifications: 53D20 - Momentum maps; symplectic reduction 55N91 - Equivariant homology and cohomology [See also 19L47] 57S15 - Compact Lie groups of differentiable transformations