Moment maps and non-compact cobordisms

Details Moment maps and non-compact cobordisms Moment maps and non-compact cobordisms

1997-01-19

arxiv.org/abs/dg-ga/9701006v1

Mathematics

Differential Geometry

LaTeX2e, 13 pages

Scientific paper

We define a moment map associated to a smooth torus action on a smooth manifold, without a two-form. We define cobordisms of such structures, allowing non compact manifolds as long as the moment maps are proper. We prove that a compact manifold with a torus action and a moment map is cobordant to the disjoint union of the normal bundles of the connected components of the fixed points set. We use this to give simple new proofs of two formulas: Guillemin's topological version of the abelian Jeffrey-Kirwan localization, and the Guillemin-Lerman-Sternberg formula for the Duistermaat-Heckman measure.

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