Delocalized Equivariant Cohomology and Resolution

نویسندگان

  • PIERRE ALBIN
  • RICHARD MELROSE
چکیده

A refined form of the ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type was established in [1] in the context of manifolds with corners; the canonical construction induces fibrations on the boundary faces of the resolution resulting in an ‘equivariant resolution structure’. Here, equivariant K-theory and the Cartan model for equivariant cohomology are tracked under the resolution procedure as is the delocalized equivariant cohomology of Baum, Brylinski and MacPherson. This leads to resolved models for each of these cohomology theories, in terms of relative objects over the resolution structure and hence to reduced models as flat-twisted relative objects over the resolution of the quotient. An explicit equivariant Chern character is then constructed, essentially as in the non-equivariant case, over the resolution of the quotient.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Equivariant Resolution, Cohomology and Index Joint Work with Pierre Albin for Werner Müller’s 60th Birthday

In this talk I describe the resolution to unique isotropy type of the smooth action of a compact Lie group as contained in joint work with Pierre Albin, [2], [3]. The resulting ‘resolution tower’ leads to resolved and reduced models for equivariant cohomology, including the delocalized cohomology of Baum, Brylinski and MacPherson, and K-theory. Combining these constructions with a lifting map g...

متن کامل

Equivariant Cohomology and Resolution

The ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types in a ‘resolution tower’ which projects to a resolution, with iterated boundary fibration, of the quotient. Equivaria...

متن کامل

Ring structures of mod p equivariant cohomology rings and ring homomorphisms between them

In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...

متن کامل

Delocalized Equivariant Cohomology of Symmetric Products

For any closed complex manifold X, we calculate the Poincaré and Hodge polynomials of the delocalized equivariant cohomology H(X, Sn) with a grading specified by physicists. As a consequence, we recover a special case of a formula for the elliptic genera of symmetric products in DijkgraafMoore-Verlinde-Verlinde [8]. For a projective surface X, our results matches with the corresponding formulas...

متن کامل

The T–equivariant Cohomology of Bott–samelson Varieties

We consider the T–equivariant cohomology of Bott–Samelson desingularisations of Schubert varieties in the flag manifold of a connected semi–simple complex algebraic group of adjoint type with maximal torus T . We construct a combinatorially pure (in the sense of T. Braden and R. Macpherson) sheaf on the Bruhat graph of the associated Weyl group such that its global sections give the T–equivaria...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010