相关论文: Semi-topological K-theory for certain projective v…

This survey deals with the construction of a category of spectral triples that is compatible with the Kasparov product in $KK$-theory. These notes serve as an intuitive guide to these results, avoiding the necessary technical proofs. We…

Given an ample groupoid, we construct a spectral sequence with groupoid homology with integer coefficients on the second sheet, converging to the K-groups of the (reduced) groupoid C*-algebra, provided the groupoid has torsion-free…

We consider groups G which have a cocompact, 3-manifold model for the classifying space \underline{E}G. We provide an algorithm for computing the rationalized equivariant K-homology of \underline{E}G. Under the additional hypothesis that…

We study the GKM theory for a equivariant stratified space having orbifold structures in tis successive quotients. Then, we introduce the notion of an \emph{almost simple polytope}, as well as a \emph{divisive toric variety} generalizing…

This thesis splits into two major parts. The connection between the two parts is the notion of "categorification" which we shortly explain/recall in the introduction. In the first part of this thesis we extend Bar-Natan's cobordism based…

We present a spectral sequence connecting the continuous and 'locally continuous' group cohomologies for topological groups. As an application it is shown that for contractible topological groups these cohomology concepts coincide. Similar…

In this thesis, we give a definition of topological K-theory of Kontsevich's noncommutative spaces (ie dg-categories) defined over the complex. The main motivation comes from noncommutative Hodge structures in the sense of…

Some aspects of the construction of SW Floer homology for manifolds with non-trivial rational homology are analyzed. In particular, the case of manifolds that are obtained as zero-surgery on a knot in a homology sphere, and for torsion…

This survey article on bivariant Kasparov theory and E-theory is mainly intended for readers with a background in homotopical algebra and category theory. We approach both bivariant K-theories via their universal properties and equip them…

In this paper, semilocal Milnor $K$-theory of fields is introduced and studied. A strongly convergent spectral sequence relating semilocal Milnor $K$-theory to semilocal motivic cohomology is constructed. In weight 2, the motivic cohomology…

We develop local cohomology techniques to study the finite slope part of the coherent cohomology of Shimura varieties. The local cohomology groups we consider are a generalization of overconvergent modular forms, and they are defined by…

This is the first in a series of papers investigating the relationship between the twisted equivariant K-theory of a compact Lie group G and the "Verlinde ring" of its loop group. In this paper we set up the foundations of twisted…

We use topological K-theory to study non-singular varieties with quadratic entry locus. We thus obtain a new proof of Russo's Divisibility Property for locally quadratic entry locus manifolds. In particular we obtain a K-theoretic proof of…

In this paper we examine certain filtrations of topological Hochschild homology and topological cyclic homology. As an example we show how the filtration with respect to a nilpotent ideal gives rise to an analog of a theorem of Goodwillie…

In this paper we prove that cyclic homology, topological cyclic homology, and algebraic $K$-theory satisfy a pro Mayer--Vietoris property with respect to abstract blow-up squares of varieties, in both zero and finite characteristic. This…

We view strict ring spectra as generalized rings. The study of their algebraic K-theory is motivated by its applications to the automorphism groups of compact manifolds. Partial calculations of algebraic K-theory for the sphere spectrum are…

We study K-theoretic Gromov--Witten invariants of projective hypersurfaces using a virtual localization formula under finite group actions. In particular, it provides all K-theoretic Gromov--Witten invariants of the quintic threefold modulo…

Smooth K-functors are introduced and the smooth K-theory of locally convex algebras is developed. It is proved that the algebraic and smooth K-functors are isomorphic on the category of quasi stable real (or complex) Frechet algebras.

Associated with a smooth, $d$-closed $(1, 1)$-form $\alpha$ of possibly non-rational De Rham cohomology class on a compact complex manifold $X$ is a sequence of asymptotically holomorphic complex line bundles $L_k$ on $X$ equipped with $(0,…

We consider correspondences on smooth quasiprojective varieties $U$. An algebraic cycle inducing the K\"unneth projector onto $H^1(U)$ is constructed. Assuming normal crossings at infinity, the existence of relative motivic cohomology is…