K-Theory and Homology
The Steenrod operations (mod p) in Chow theory are defined for any prime p for a quasi-projective scheme, without appealing to the results of any domain but Milnor's K-theory. The new definition also gives a direct formula that depends only…
We obtain a mixed complex, simpler that the canonical one, given the Hochschild, cyclic, negative and periodic homology of a crossed product E=A#fH, where H is an arbitrary Hopf algebra and f is a convolution invertible cocycle with values…
We show that the Baum-Connes morphism twisted by a non-unitary representation, defined in [GA08], is an isomorphism for a large class of groups satisfying the Baum-Connes conjecture. Such class contains all the real semi-simple Lie groups,…
We define a group of relative differential K-characters associated with a smooth map between two smooth compact manifolds. We show that this group fits into a short exact sequence as in the non-relative case. Some secondary geometric…
The paper explores some algebraic constructions arising in the theory of Lefschetz fibrations. Specifically, it covers in a fair amount of detail the algebraic issues outlined in ``Symplectic homology as Hochschild homology''…
We formulate a "correct" version of the Quillen conjecture on linear group homology for certain arithmetic rings and provide evidence for the new conjecture. In this way we predict that the linear group homology has a direct summand looking…
In this paper we define higher pre-Bloch groups p_n(F) of a field F. When our base field is algebraically closed we study its connection to the homology of the general linear groups with finite coefficient Z/l where l is a positive integer.…
The homology of GL_n(F) and SL_n(F) is studied, where F is an infinite field. Our main theorem states that the natural map H_4(GL_3(F), k) --> H_4(GL_4(F), k) is injective where k is a field with char(k) \neq 2, 3. For algebraically closed…
We prove homological stability for standard unitary groups over R, C and H and for general linear groups over skew-fields with infinite centre. We focus on the similarities and differences of these proofs. Both proofs are due to Chih-Han…
It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extend this is still true. We give an explicit description of the…
In this paper, we introduce a notion of weight r pseudo-coherent Modules associated to a regular closed immersion i:Y -> X of codimension r, and prove that there is a canonical derived Morita equivalence between the DG-category of perfect…
For any Lie groupoid we construct an analytic index morphism taking values in a modified $K-theory$ group which involves the convolution algebra of compactly supported smooth functions over the groupoid. The construction is performed by…
This note explains consequences of recent work of Frank Quinn for computations of Nil groups in algebraic K-theory, in particular the Nil groups occurring in the K-theory of polynomial rings, Laurent polynomial rings, and the group ring of…
In this paper, we compute the Poisson (co)homology of a polynomial Poisson structure given by two Casimir polynomial functions which define a complete intersection with an isolated singularity.
The isomorphism of 0-homology groups of a categorical at zero semigroup and homology groups of its 0-reflector is proved. Some applications of 0-homology to Eilenberg-MacLane homology of semigroups are given.
This is an expository account of the following result: we can construct a group by means of twisted Z_2-graded vectorial bundles which is isomorphic to K-theory twisted by any degree three integral cohomology class.
We modify the definition of l^1-homology and argue why our definition is more adequate than the classical one. While we cannot reconstruct the classical l^1-homology from the new definition for various reasons, we can reconstruct its…
This paper presents, by example, an index theory appropriate to algebras without trace. Whilst we work exclusively with the Cuntz algebras the exposition is designed to indicate how to develop a general theory. Our main result is an index…
We consider cohomology of diagrams of algebras by Beck's approach, using comonads. We then apply this theory to computing the cohomology of $\Psi$-rings. Our main result is that there is a spectral sequence connecting the cohomology of the…
A chain of c submodules E =: E_0 >= E_1 >= ... >= E_c >= E_{c+1} := 0 gives rise to c composable 1-cocycles in Ext^1(E_{i-1}/E_i,E_i/E_{i+1}), i=1,...,c. In this paper we follow the converse question: When are c composable 1-cocycles…