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

Authors

  • Yanchang Chen College of Mathematics and Information Science, Hebei Normal University, Yuhua Road 113, Shijiazhuang 050016, P. R. China
  • Yanying Wang College of Mathematics and Information Science, Hebei Normal University, Yuhua Road 113, Shijiazhuang 050016, P. R. China
Abstract:

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 it possible to determine the number of equivariant cohomology rings (up to isomorphism) of such 2-dimensional G-manifolds. Moreover, we obtain a description of the ring homomorphism between equivariant cohomology rings of such two G-manifolds induced by a G-equivariant map, and show a characterization of the ring homomorphism.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

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 it p...

full text

Stability and hyperstability of orthogonally ring $*$-$n$-derivations and orthogonally ring $*$-$n$-homomorphisms on $C^*$-algebras

In this paper, we investigate the generalized Hyers-Ulam-Rassias and the Isac and Rassias-type stability of the conditional of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras. As a consequence of this, we prove the hyperstability of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras.

full text

Equivariant Cohomology and Analytic Descriptions of Ring Isomorphisms

In this paper we consider a class of connected closed G-manifolds with a non-empty finite fixed point set, each M of which is totally non-homologous to zero in MG (or G-equivariantly formal), where G = Z2. With the help of the equivariant index, we give an explicit description of the equivariant cohomology of such a G-manifold in terms of algebra, so that we can obtain analytic descriptions of ...

full text

Mod-two Cohomology of Symmetric Groups as a Hopf Ring

On the cohomology of BS• the second product · is cup product, which is zero for classes supported on disjoint components. The first product ⊙ is the relatively new transfer product first studied by Strickland and Turner [21], (see Definition 3.1). It is akin to the “induction product” in the representation theory of symmetric groups, which dates back to Young and has been in standard use [9, 22...

full text

On the Spectrum of the Equivariant Cohomology Ring

If an algebraic torus T acts on a complex projective algebraic variety X then the affine scheme Spec H∗ T (X;C) associated to the equivariant cohomology is often an arrangement of linear subspaces of the vector space H 2 (X;C). In many situations the ordinary cohomology ring of X can be described in terms of this arrangement.

full text

Augmentation Ideals of Equivariant Cohomology Rings

The purpose of this note is to establish a number of useful results about the augmentation ideal J for the coefficient ring F ∗ G of a Noetherian complex orientable equivariant cohomology theory. The results show that various naturally occurring substitutes for the ideal have the same radical, and can therefore be used instead of the augmentation ideal in all geometric constructions. 1. Stateme...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 38  issue 2

pages  529- 542

publication date 2012-07-15

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023