Related papers: The Hochschild-Kostant-Rosenberg isomorphism for q…
We introduce a class of normal complex spaces having only mild sin-gularities (close to quotient singularities) for which we generalize the notion of a (analytic) fundamental class for an analytic cycle and also the notion of a relative…
We apply the techniques of totally twisted Khovanov homology to the constructions by M. Asaeda, J. Przytycki, and A. Sikora of Khovanov type homologies for links and tangles in I-bundles over (orientable) surfaces. As a result we describe…
Proofs of Tsygan's formality conjectures for chains would unlock important algebraic tools which might lead to new generalizations of the Atiyah-Patodi-Singer index theorem and the Riemann-Roch-Hirzebruch theorem. Despite this pivotal role…
In this paper, we study the Hochschild cohomology of diagrams of algebras introduced by Gerstenhaber and Schack and provide computations for filtrations of incidence algebras. Our aims are threefold: firstly, we revisit and explore the…
We discuss a matrix of periodic holomorphic functions in the upper and lower half-plane which can be obtained from a factorization of an Andersen-Kashaev state integral of a knot complement with remarkable analytic and asymptotic properties…
Given an action of a Lie group on a smooth manifold, we discuss the induced action on the Hochschild cohomology of smooth functions, and notions of invariance on this space. Depending on whether one considers invariance of cochains or…
In this paper we study the regularized analytic torsion of finite volume hyperbolic manifolds. We consider sequences of coverings $X_i$ of a fixed hyperbolic orbifold $X_0$. Our main result is that for certain sequences of coverings and…
We consider diffeomorphisms $f$ with heterodimensional cycles of co-index two, associated with saddles $P$ and $Q$ having unstable indices $\ell$ and $\ell+2$, respectively. In a partially hyperbolic setting, where a two-dimensional center…
We present a brief overview of the Kor\'anyi-Reimann theory of quasiconformal mappings on the Heisenberg group stressing on the analogies as well as on the differences between the Heisenberg group case and the classical two-dimensional…
In [36, Section 8], the present author proposed the hypergraph obstruction for the existence of k-regular embeddings. In this paper, we develop the hypergraph obstruction concretely and give some homological obstructions for the k-regular…
Let $A$ be a commutative algebra over the field ${\mathbb F}_2 = {\mathbb Z}/2$. We show that there is a natural algebra homomorphism $\ell (A) \to HC^-_*(A)$ which is an isomorphism when $A$ is a smooth algebra. Thus, the functor $\ell$…
For the non-gradient exclusion process, we prove the quantitative homogenization of the diffusion matrix and the conductivity by local functions. The proof relies on the renormalization approach developed by Armstrong, Kuusi, Mourrat, and…
This paper is devoted to study multiplicity and regularity as well as to present some classifications of complex analytic sets. We present an equivalence for complex analytical sets, namely blow-spherical equivalence and we receive several…
Rational curves on Hilbert schemes of points on $K3$ surfaces and generalised Kummer manifolds are constructed by using Brill-Noether theory on nodal curves on the underlying surface. It turns out that all wall divisors can be obtained, up…
We study the cup product on the Hochschild cohomology of the stack quotient [X/G] of a smooth quasi-projective variety X by a finite group G. More specifically, we construct a G-equivariant sheaf of graded algebras on X whose G-invariant…
The paper introduces a partial integration map from the first Hochschild cohomology of any cohomologically unital A-infinity category over a field of characteristic zero to its derived Picard group. We discuss useful properties such as…
Suppose $X^{N}$ is a closed oriented manifold, $\alpha \in H^*(X;\mathbb{R})$ is a cohomology class, and $Z \in H_{N-k}(X)$ is an integral homology class. We ask the following question: is there an oriented embedded submanifold $Y^{N-k}…
We show that the Hochschild-Kostant-Rosenberg map from the space of multivector fields on a graded manifold N (endowed with a Berezinian volume) to the cohomology of the algebra of multidifferential operators on N (as a subalgebra of the…
Graph cocycles for star-products are investigated from the combinatorial point of view, using Connes-Kreimer renormalization techniques. The Hochschild complex, controlling the deformation theory of associative algebras, is the ``Kontsevich…
Covariant integral quantizations are based on the resolution of the identity by continuous or discrete families of normalised positive operator valued measures (POVM), which have appealing probabilistic content and which transform in a…