Related papers: AF-equivalence relations and their cocycles

One of the themes in algebraic geometry is the study of the relation between the ``topology'' of a smooth projective variety and a (``general'') hyperplane section. Recent results of Nori produce cohomological evidence for a conjecture that…

We introduce the notion of cyclic cohomology of an A-infinity algebra and show that the deformations of an A-infinity algebra which preserve an invariant inner product are classified by this cohomology. We use this result to construct some…

Every homology or cohomology theory on a category of E-infinity ring spectra is Topological Andre-Quillen homology or cohomology with appropriate coefficients. Analogous results hold for the category of A-infinity ring spectra and for…

We define the rigid homology. The trace morphism in rigid cohomology define by duality the cycle class in rigid homology. We verify the compatibility of this classes with rationnal equivalence and intersection theory. We deduce some formal…

In this paper we present the construction of explicit quasi-isomorphisms that compute the cyclic homology and periodic cyclic homology of crossed-product algebras associated with (discrete) group actions. In the first part we deal with…

We consider the horocyclic flow corresponding to a (topologically mixing) Anosov flow or diffeomorphism, and establish the uniqueness of transverse quasi-invariant measures with H\"older Jacobians. In the same setting, we give a precise…

We prove that certain Gibbs measures on subshifts of finite type are nonsingular and ergodic for certain countable equivalence relations, including the orbit relation of the adic transformation (the same as equality after a permutation of…

We define a noncommutative analogue of invariant de Rham cohomology. More precisely, for a triple $(A,\mathcal{H},M)$ consisting of a Hopf algebra $\mathcal{H}$, an $\mathcal{H}$-comodule algebra $A$, an $\mathcal{H}$-module $M$, and a…

We give explicit formulae for the continuous Hochschild and cyclic homology and cohomology of certain topological algebras. To this end we show that, for a continuous morphism $\phi: \X\to \Y$ of complexes of complete nuclear $DF$-spaces,…

Connections between partial dynamcial systems, a generalized notion of partial dynamical systems defined by nested sequences of partial homeomorphisms, and triangular AF algebras which admit an integer-valued cocycle are established.

We consider inclusions $\mathcal{S}\leq \mathcal{R}$ of discrete, probability measure-preserving orbit equivalence relations. In previous work with Ab\'{e}rt-Fra\c{c}zyk, we established the pointwise almost sure existence of the cospectral…

We introduce the notions of approximate cohomology and approximate homotopy in Banach algebras and we study the relation between them. We show that the approximate homotopically equivalent cochain complexes give the same approximate…

Lines and circles pose significant scalability challenges in synthetic geometry. A line with $n$ points implies ${n \choose 3}$ collinearity atoms, or alternatively, when lines are represented as functions, equality among ${n \choose 2}$…

W. Arveson has described a cocycle conjugacy class $U(\alpha)$ of $E_0$-semigroup $\alpha$ on B(H) which is a factor of type $\rm I$. Under some conditions on $\alpha$, there is a $E_0$-semigroup $\beta \in U(\alpha)$ being a flow of shifts…

This is a report on the present state of the problem of determining the dimension of the Nichols algebra associated to a rack and a cocycle. This is relevant for the classification of finite-dimensional complex pointed Hopf algebras whose…

We continue the research of the relation $\hspace{1mm}\widetilde{\mid}\hspace{1mm}$ on the set $\beta {\mathbb{N}}$ of ultrafilters on ${\mathbb{N}}$, defined as an extension of the divisibility relation. It is a quasiorder, so we see it as…

A cohomology theory is proposed for the recently discovered heptagon relation -- an algebraic imitation of a 5-dimensional Pachner move 4--3. In particular, `quadratic cohomology' is introduced, and it is shown that it is quite nontrivial,…

Let A be any finite dimensional Hopf algebra over a field k. We specify the Tate and Tate-Hochschild cohomology for A and introduce cup products that make them become graded rings. We establish the relationship between these rings. In…

We consider associative superalgebra realized on the smooth Grassmann-valued functions with compact supports in R^n. The lower Hochschild cohomologies of this superalgebra are found.

Given a henselian pair $(R, I)$ of commutative rings, we show that the relative $K$-theory and relative topological cyclic homology with finite coefficients are identified via the cyclotomic trace $K \to \mathrm{TC}$. This yields a…