相关论文: A Functor Converting Equivariant Homology to Homot…

Freed, Hopkins and Teleman constructed an isomorphism between twisted equivariant K-theory of compact Lie group $G$ and the "Verlinde ring" of the loop group of $G$. We call this isomorphism FHT isomorphism. However, it does not hold…

Let $M$ be a monoid and $G:\mathbf{Mon} \to \mathbf{Grp}$ be the group completion functor from monoids to groups. Given a collection $\mathcal{X}$ of submonoids of $M$ and for each $N\in \mathcal{X}$ a collection $\mathcal{Y}_N$ of…

Lie groupoids generalize transformation groups, and so provide a natural language for studying orbifolds and other noncommutative geometries. In this paper, we investigate a connection between orbifolds and equivariant stable homotopy…

We show that the main theorem of Morse theory holds for a large class of functions on singular spaces. The function must satisfy certain conditions extending the usual requirements on a manifold that Condition C holds and the gradient flow…

In this paper, we study the equivariant homotopy type of a connected sum of linear actions on complex projective planes defined by Hambleton and Tanase. These actions are constructed for cyclic groups of odd order. We construct cellular…

Let $X$ be a simply connected path connected topological space which is formal in the sense of rational homotopy theory. Let $Y=X\cup_\alpha\mathbb{D}^{n}$ where $\alpha:\mathbb{S}^{n-1}\to X$ is a non-torsion element. Then we obtain a…

Let $R$ be a principal ideal domain (PID). For a simply connected CW-complex $X$ of dimension $n$, let $Y$ be a space obtained by attaching cells of dimension $q$ to $X$, $q>n$, and let $A(Y)$ denote an Adams-Hilton model of $Y$. If…

We prove new structural results for the rational homotopy type of the classifying space $B\operatorname{aut}(X)$ of fibrations with fiber a simply connected finite CW-complex $X$. We first study nilpotent covers of $B\operatorname{aut}(X)$…

We present a way of constructing and deforming diffeomorphisms of manifolds endowed with a Lie group action. This is applied to the study of exotic diffeomorphisms and involutions of spheres and to the equivariant homotopy of Lie groups.

We study the eigenforms of the action of A. Baker's Hecke operators on the holomorphic elliptic homology of various topological spaces. We prove a multiplicity one theorem (i.e., one-dimensionality of the space of these "topological Hecke…

For T an abelian compact Lie group, we give a description of T-equivariant K-theory with complex coefficients in terms of equivariant cohomology. In the appendix we give applications of this by extending results of Chang-Skjelbred and…

We introduce a new construction, the isotropy groupoid, to organize the orbit data for split $\Gamma$-spaces. We show that equivariant principal $G$-bundles over split $\Gamma$-CW complexes $X$ can be effectively classified by means of…

In this article, we define the l-adic homology for a morphism of schemes satisfying certain finiteness conditions. This homology has these functors similar to the Chow groups: proper push-forward, flat pull-back, base change, cap-product,…

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…

We study the semi-topologization functor of Friedlander-Walker from the perspective of motivic homotopy theory. We construct a triangulated endo-functor on the stable motivic homotopy category $\mathcal{SH}(\C)$, which we call…

One proves that the category of globular CW-complexes up to dihomotopy is equivalent to the category of flows up to weak dihomotopy. This theorem generalizes the classical theorem which states that the category of CW-complexes up to…

Using methods applied by Atiyah in equivariant K-theory, Bredon obtained exact sequences for the relative cohomologies (with rational coefficients) of the equivariant skeletons of (sufficiently nice) T-spaces, T=(S^1)^n, with free…

We introduce the notion of a Bredon-style equivariant coarse homology theory. We show that such a Bredon-style equivariant coarse homology theory satisfies localization theorems and that a general equivariant coarse homology theory can be…

We explore some of the special features with respect to Bredon cohomology of groups having all its finite subgroups either nilpotent or p-groups or cyclic p-groups. We get some results on dimensions and also a formula for the equivariant…

This is a further investigation of our approach to group actions in homological algebra in the settings of homology of {\Gamma}-simplicial groups, particularly of {\Gamma}-equivariant homology and cohomology of {\Gamma}-groups. This…