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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/9389

Title: Localization theorems by symplectic cuts
Authors: Jeffrey, Lisa Claire
Kogan, Mikhail
Keywords: Momentum maps; symplectic reduction
Equivariant homology and cohomology
Symplectic and contact topology
Issue Date: 2005
Publisher: Progress in Mathematics
Series/Report no.: 232
Abstract: Abstract. Given a compact symplectic manifold M with the Hamiltonian action of a torus T, let zero be a regular value of the moment map, and M0 the symplectic reduction at zero. Denote by 0 the Kirwan map H T (M) ! H(M0). For an equivariant cohomology class 2 H T (M) we present new localization formulas which express RM0 0() as sums of certain integrals over the connected components of the fixed point set MT . To produce such a formula we apply a residue operation to the Atiyah-Bott-Berline-Vergne localization formula for an equivariant form on the symplectic cut of M with respect to a certain cone, and then, if necessary, iterate this process using other cones. When all cones used to produce the formula are one-dimensional we recover, as a special case, the localization formula of Guillemin and Kalkman [GK]. Using similar ideas, for a special choice of the cone (whose dimension is equal to that of T) we give a new proof of the Jeffrey-Kirwan localization formula [JK1].
Description: This paper is dedicated to Alan Weinstein on the occasion of his 60th birthday.
URI: http://hdl.handle.net/1807/9389
Appears in Collections:Mathematics

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