LOCAL MODELS FOR SMOOTH TORAL ACTIONS AND RESIDUES

[摘要] If G is a compact Lie group acting smoothly on a manifold M, we prove that a G-invariant neighbourhood of the singular set Sigma in M is completely determined by the G-vector bundle restriction of the tangent bundle of M to Sigma, Moreover, by using only this G-vector bundle we define a residual linear map, above certain degrees, giving the Chern-Weil homomorphism for M, after composing it in cohomology with the inclusion of M in (M, M - Sigma). In the case of G being a torus, we characterize those G-vector bundles appearing as restriction to the singular set of the tangent bundle of some smooth G-manifold.

[发布日期] 1994-01-17