Related papers: Equivariant K-theory and Resolution I: Abelian act…

We study Hamiltonian actions of compact Lie groups K on Kaehler manifolds which extend to a holomorphic action of the complexified group K^C. For a closed normal subgroup L of K we show that the Kaehlerian reduction with respect to L is a…

Inspired by the work of Chevalley and Eilenberg on the de Rham cohomology on compact Lie groups, we prove that, under certain algebraic and topological conditions, the cohomology associated to left-invariant elliptic, and even hypocomplex,…

Let G denote a compact connected Lie group with torsion-free fundamental group acting on a compact space X such that all the isotropy subgroups are connected subgroups of maximal rank. Let $T\subset G$ be a maximal torus with Weyl group W.…

Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…

For a smooth (locally trivial) principal bundle in Ehresmann's sense, the relation between the commuting vertical and horizontal actions of the structural Lie group and the structural Lie groupoid (isomorphisms between vertical fibers) is…

We define equivariant projective unitary stable bundles as the appropriate twists when defining K-theory as sections of bundles with fibers the space of Fredholm operators over a Hilbert space. We construct universal equivariant projective…

In this paper, we develop a new method to classify abelian automorphism groups of hypersurfaces. We use this method to classify (Theorem 4.2) abelian groups that admit a liftable action on a smooth cubic fourfold. A parallel result (Theorem…

Kitchloo and Morava give a strikingly simple picture of elliptic cohomology at the Tate curve by studying a completed version of $S^1$-equivariant $K$-theory for spaces. Several authors (cf [ABG],[KM],[L]) have suggested that an equivariant…

Suppose that a compact quantum group Q acts faithfully and isomet- rically (in the sense of [10]) on a smooth compact, oriented, connected Riemannian manifold M . If the manifold is stably parallelizable then it is shown that the compact…

It was shown by Samelson and Wang that each compact Lie group K of even dimension admits left-invariant complex structures. When K has odd dimension it admits a left-invariant CR-structure of maximal dimension. This has been proved recently…

We introduce and study a $K$-theory of twisted bundles for associative algebras $A(\mathfrak g)$ of formal series with an infinite-Lie algebra coefficients over arbitrary compact topological spaces. Fibers of such bundles are given by…

Let $G$ be a connected algebraic $k$-group acting on a normal $k$-variety, where $k$ is a field. We show that $X$ is covered by open $G$-stable quasi-projective subvarieties; moreover, any such subvariety admits an equivariant embedding…

Let $X$ be a topological space upon which a compact connected Lie group $G$ acts. It is well-known that the equivariant cohomology $H_G^*(X;\Q)$ is isomorphic to the subalgebra of Weyl group invariants of the equivariant cohomology…

In topology there is a theorem of Atiyah, concerning K-theory of classifying space of connected compact Lie group. We consider an algebraic analogue of this theorem. We prove that for a split reductive algebraic group G over a field there…

Let G be a compact, connected Lie group, acting smoothly on a manifold M. Goresky-Kottwitz-MacPherson described a small Cartan model for the equivariant cohomology of M, quasi-isomorphic to the standard Cartan complex of equivariant…

For any abelian compact Lie group $G$, we introduce a family of $G$-stratified pseudomanifolds, whose main feature is the preservation of the orbit spaces in the category of stratified pseudomanifolds. Which generalize a previous definition…

We show that for every symmetric space G/K of compact type with K connected, the K-action on G/K by left translations is equivariantly formal.

We study Cohen-Macaulay actions, a class of torus actions on manifolds, possibly without fixed points, which generalizes and has analogous properties as equivariantly formal actions. Their equivariant cohomology algebras are computable in…

We prove the deformation invariance of the quantum homogeneous spaces of the q-deformation of simply connected simple compact Lie groups over the Poisson-Lie quantum subgroups, in the equivariant KK-theory with respect to the translation…

We compare different algebraic structures in twisted equivariant K-Theory for proper actions of discrete groups. After the construction of a module structure over untwisted equivariant K-Theory, we prove a completion Theorem of Atiyah-Segal…