Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-09T15:22:22.810Z Has data issue: false hasContentIssue false

INVARIANT SULLIVAN–DE RHAM FORMS ON CYCLIC SETS

Published online by Cambridge University Press:  01 April 1998

CHRISTOPHER ALLDAY
Affiliation:
Department of Mathematics, University of Hawaii at Manoa, 2565 The Mall, Honolulu, Hawaii 96822
Get access

Abstract

Let Y be a topological space; and suppose that the circle group, S1, which will be denoted by G throughout this paper, is acting on Y. Then the equivariant cohomology H*G(Y) of Y is defined to be H*(YG), where YG=(EG×Y)/G, the Borel construction. Because of the bundle map YGBG, the cohomology H*G(Y) is an H*(BG)-module. With rational coefficients H*(BG; ℚ)=ℚ[u], where deg(u)=2. And, when Y is a reasonably nice finite-dimensional space, for example, a finite-dimensional G-CW-complex, then the localized module H*G(Y; ℚ)[u−1] is isomorphic to H*G (YG; ℚ)[u−1] via the restriction homomorphism, where YGY is the fixed point set. (See, for example, [2].) That this very useful Localization Theorem does not generalize to infinite dimensional spaces can be seen by taking Y=EG, for example.

Type
Notes and Papers
Copyright
The London Mathematical Society 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)