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On localization in holomorphic equivariant cohomology

Ugo Bruzzo, Vladimir Rubtsov (2012)

Open Mathematics

We study a holomorphic equivariant cohomology built out of the Atiyah algebroid of an equivariant holomorphic vector bundle and prove a related localization formula. This encompasses various residue formulas in complex geometry, in particular we shall show that it contains as special cases Carrell-Liebermann’s and Feng-Ma’s residue formulas, and Baum-Bott’s formula for the zeroes of a meromorphic vector field.

Orbit spaces, Quillen's Theorem A and Minami's formula for compact Lie groups

Assaf Libman (2011)

Fundamenta Mathematicae

Let G be a compact Lie group. We present a criterion for the orbit spaces of two G-spaces to be homotopy equivalent and use it to obtain a quick proof of Webb’s conjecture for compact Lie groups. We establish two Minami type formulae which present the p-localised spectrum Σ B G as an alternating sum of p-localised spectra Σ B H for subgroups H of G. The subgroups H are calculated from the collections of the non-trivial elementary abelian p-subgroups of G and the non-trivial p-radical subgroups of G. We...

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