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Search: MSC category 53D20 ( Momentum maps; symplectic reduction )

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1. CMB 2007 (vol 50 pp. 365)

Godinho, Leonor
Equivariant Cohomology of $S^{1}$-Actions on $4$-Manifolds
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.

Categories:53D20, 55N91, 57S15

2. CMB 2005 (vol 48 pp. 561)

Foth, Philip
A Note on Lagrangian Loci of Quotients
We study Hamiltonian actions of compact groups in the presence of compatible involutions. We show that the Lagrangian fixed point set on the symplectically reduced space is isomorphic to the disjoint union of the involutively reduced spaces corresponding to involutions on the group strongly inner to the given one. Our techniques imply that the solution to the eigenvalues of a sum problem for a given real form can be reduced to the quasi-split real form in the same inner class. We also consider invariant quotients with respect to the corresponding real form of the complexified group.

Keywords:Quotients, involutions, real forms, Lagrangian loci
Category:53D20

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