Related papers: Equivariant formality of istropy actions

Recent work of Chen He has determined through GKM methods the Borel equivariant cohomology with rational coefficients of the isotropy action on a real Grassmannian and an real oriented Grassmannian through GKM methods. In this expository…

We define and discuss G-formality for certain spaces endowed with an action by a compact Lie group. This concept is essentially formality of the Borel construction of the space in a category of commutative differential graded algebras over…

We give a proof of Kontsevich's formality theorem for a general manifold using Fedosov resolutions of algebras of polydifferential operators and polyvector fields. The main advantage of our construction of the formality quasi-isomorphism is…

We develop equivariant KK-theory for locally compact groupoid actions by Morita equivalences on real and complex graded C*-algebras. Functoriality with respect to generalised morphisms and Bott periodicity are discussed. We introduce…

Let $G$ be a compact, connected, and simply-connected Lie group, equipped with a Lie group involution $\sigma_G$ and viewed as a $G$-space with the conjugation action. In this paper, we present a description of the ring structure of the…

We give a new proof of the universal property of $KK^G$-theory with respect to stability, homotopy invariance and split-exactness for $G$ a locally compact group, or a locally compact (not necessarily Hausdorff) groupoid, or a countable…

Generalizing a construction of Wolfgang L\"uck and Bob Oliver, we define a good equivariant cohomology theory on the category of proper G-CW complexes when G is an arbitrary Lie group (possibly non-compact). This is done by constructing an…

We develop the foundations of $G$-global homotopy theory as a synthesis of classical equivariant homotopy theory on the one hand and global homotopy theory in the sense of Schwede on the other hand. Using this framework, we then introduce…

We provide and study an equivariant theory of group (co)homology of a group G with coefficients in a gamma-equivariant G-module A, when a separate group "gamma" acts on G and A, generalizing the classical Eilenberg-MacLane (co)homology of…

For a compact simply connected simple Lie group $G$ with an involution $\alpha$, we compute the $G\rtimes \Z/2$-equivariant K-theory of $G$ where $G$ acts by conjugation and $\Z/2$ acts either by $\alpha$ or by $g\mapsto \alpha(g)^{-1}$. We…

We prove a decomposition theorem for the equivariant K-theory of actions of affine group schemes G of finite type over a field on regular separated noetherian algebraic spaces, under the hypothesis that the actions have finite geometric…

This monograph introduces a framework for genuine proper equivariant stable homotopy theory for Lie groups. The adjective `proper' alludes to the feature that equivalences are tested on compact subgroups, and that the objects are built from…

We consider twisted equivariant K--theory for actions of a compact Lie group $G$ on a space $X$ where all the isotropy subgroups are connected and of maximal rank. We show that the associated rational spectral sequence \`a la Segal has a…

The smooth action of a compact Lie group on a compact manifold can be resolved to an iterated space, as made explicit by Pierre Albin and the second author. On the resolution the lifted action has fixed isotropy type, in an iterated sense,…

We give a characterization of those Alexandrov spaces admitting a cohomogeneity one action of a compact connected Lie group $G$ for which the action is Cohen--Macaulay. This generalizes a similar result for manifolds to the singular setting…

For an arbitrary compact Lie group G, we describe a model for rational G-spectra with toral geometric isotropy and show that there is a convergent Adams spectral sequence based on it. The contribution from geometric isotropy at a subgroup K…

In a previous paper, we have constructed, for an arbitrary Lie group G and any of the fields F=R or C, a good equivariant cohomology theory KF_G^*(-) on the category of proper $G$-CW-complex and have justified why it deserved the label…

Following Hopkins and Singer, we give a definition for the differential equivariant K-theory of a smooth manifold acted upon by a finite group. The ring structure for differential equivariant K-theory is developed explicitly. We also…

This is a survey on the equivariant cohomology of Lie group actions on manifolds, from the point of view of de Rham theory. Emphasis is put on the notion of equivariant formality, as well as on applications to ordinary cohomology and to…

Algebraic models for equivariant rational homotopy theory were developed by Triantafillou and Scull for finite group actions and $S^1$ action, respectively. They showed that given a diagram of rational cohomology algebras from the orbit…