K理论与同调

With the help of the tools of Quillen's homotopical algebra, we construct `the universal additive invariant', namely a functor from the category of small dg categories to an additive category, that inverts the Morita dg functors, transforms…

We relate Leibniz homology to cyclic homology by studying a map from a long exact sequence in the Leibniz theory to the ISB periodicity sequence in the cyclic theory. This provides a setting by which the two theories can be compared via the…

We define certain class of correspondences of polarized representations of $C^*$-algebras. Our correspondences are modeled on the spaces of boundary values of elliptic operators on bordisms joining two manifolds. In this setup we define the…

In a previous paper we have introduced the gauge-equivariant K-theory group of a bundle endowed with a continuous action of a bundle of compact Lie groups. These groups are the natural range for the analytic index of a family of…

For an orbifold X and $\alpha \in H^3(X, Z)$, we introduce the twisted cohomology $H^*_c(X, \alpha)$ and prove that the Connes-Chern character establishes an isomorphism between the twisted K-groups $K_\alpha^* (X) \otimes C$ and twisted…

We give a new construction of cyclic homology of an associative algebra A that does not involve Connes' differential. Our approach is based on an extended version of the complex \Omega A, of noncommutative differential forms on A, and is…

It is shown that the class of Fredholm operators over an arbitrary unital $C^{*}$--algebra, which may not admit adjoint ones, can be extended in such a way that this class of compact operators, used in the definition of the class of…

The goal of the present paper is the calculation of the equivariant twisted K-theory of a compact Lie group which acts on itself by conjugations, and elements of a TQFT-structure on the twisted K-groups. These results are originally due to…

We consider algebras over a field $k$ of characteristic zero. The article is concerned with the isomorphism of graded vectorspaces \[ H(\gl(A))\iso\wedge (HC(A)[-1]) \] between the Lie algebra homology of matrices and the free graded…

We prove that "unitary deformation K-theory" takes products of finitely generated groups to coproducts of algebra spectra over ku, the connective K-theory spectrum. Additionally, we give spectral sequences for computing the homotopy groups…

We consider functors from the category of locally convex algebras to abelian groups and prove invariance under smooth homotopies for weakly J-stable algebras, where J is a harmonic operator ideal. This applies in particular to negative…

A recollement of triangulated categories describes one such category as being "glued together" from two others. This paper gives a precise criterion for the existence of a recollement of the derived category of a Differential Graded Algebra…

We compute the completion of the special linear group over the coordinate ring of a curve over a number field $k$ relative to its representation in $\slnk$, and relate this to the study of $K_2$ of the curve.

A graphs of rank n (homotopy equivalent to a wedge of n circles) without ``separating edges'' has a canonical n-dimensional compact C^1 manifold thickening. This implies that the canonical homomorphism f:Out(F_n)-> GL(n,Z) is trivial in…

The main objectives of this paper are to give general proofs of the following two facts: A. For an operad $\oo$ in $\ab$, let $A$ be a simplicial $\oo$-algebra such that $A_m$ is the $\oo$-subalgebra generated by $(\sum_{i = 0}^{m}…

A central result here is the computation of the entire cyclic homology of canonical smooth subalgebras of stable continuous trace C*-algebras having smooth manifolds M as their spectrum. More precisely, the entire cyclic homology is shown…

In this article, the cyclic homology theory of formal deformation quantizations of the convolution algebra associated to a proper etale Lie groupoid is studied. We compute the Hochschild cohomology of the convolution algebra and express it…

Using the unbounded picture of analytical K-homology, we associate a well-defined K-homology class to an unbounded symmetric operator satisfying certain mild technical conditions. We also establish an ``addition formula'' for the Dirac…

We consider smooth actions of totally disconnected groups on simplicial complexes and compare different equivariant cohomology groups associated to such actions. Our main result is that the bivariant equivariant cohomology theory introduced…

We define and study equivariant periodic cyclic homology for locally compact groups. This can be viewed as a noncommutative generalization of equivariant de Rham cohomology. Although the construction resembles the Cuntz-Quillen approach to…