On the localization formula in equivariant cohomology |
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Authors: | Andrés Pedroza Loring W Tu |
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Institution: | a Facultad de Ciencias, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Col., Mexico 28045 b Department of Mathematics, Tufts University, Medford, MA 02155, USA |
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Abstract: | We give a generalization of the Atiyah-Bott-Berline-Vergne localization theorem for the equivariant cohomology of a torus action. We replace the manifold having a torus action by an equivariant map of manifolds having a compact connected Lie group action. This provides a systematic method for calculating the Gysin homomorphism in ordinary cohomology of an equivariant map. As an example, we recover a formula of Akyildiz-Carrell for the Gysin homomorphism of flag manifolds. |
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Keywords: | primary 55N25 57S15 secondary 14M15 |
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