Related papers: Delooping levels
On a (pseudo-)Riemannian manifold (MM,g), some fields of endomorphisms i.e. sections of End(TMM) may be parallel for g. They form an associative algebra A, which is also the commutant of the holonomy group of g. As any associative algebra,…
The level of a module over a differential graded algebra measures the number of steps required to build the module in an appropriate triangulated category. Based on this notion, we introduce a new homotopy invariant of spaces over a fixed…
We introduce a new type of reduction of inversive difference polynomials that is associated with a partition of the basic set of automorphisms $\sigma$ and uses a generalization of the concept of effective order of a difference polynomial.…
Let $X$ be a 3-dimensional affine variety with a faithful action of a 2-dimensional torus $T$. Then the space of first order infinitesimal deformations $T^1(X)$ is graded by the characters of $T$, and the zeroth graded component $T^1(X)_0$…
We show that the Elliott invariant is a classifying invariant for the class of $C^*$-algebras that are simple unital infinite dimensional inductive limits of sequences of finite direct sums of building blocks of the form $$ \{f\in…
We show that the distance from an element of a C*-algebra to the set of regular elements is the infimum of the $\delta>0$ for which the $\delta$-cut-down of the element admits a polar decomposition within the algebra. This parallels results…
We establish a unified group-theoretic framework bridging the arithmetic homotopy exact sequence of a variety and the Birman exact sequence of a surface. Within this framework, we reinterpret classical arithmetic notions - such as the…
There appeared not long ago a Reduction Formula for derived Hochschild cohomology, that has been useful e.g., in the study of Gorenstein maps and of rigidity w.r.t. semidualizing complexes. The formula involves the relative dualizing…
We introduce a homology surgery problem in dimension 3 which has the property that the vanishing of its algebraic obstruction leads to a canonical class of \pi-algebraically-split links in 3-manifolds with fundamental group \pi . Using this…
Based on the fact that every finite-dimensional algebra over a field is isomorphic to the centralizer of \textbf{two} matrices, we approach the representation theory of finite-dimensional algebras over fields by centralizers of matrices.…
A key ingredient in the Taylor-Wiles proof of Fermat last theorem is the classical Ihara's lemma which is used to rise the modularity property between some congruent galoisian representations. In their work on Sato-Tate,…
We study holonomic modules for the rings of invariant differential operators on affine commutative domains with finite Krull dimension with respect to arbitrary actions of finite groups. We prove the Bernstein inequality for these rings.…
We introduce the framework of discrete holomorphic functions on t-embeddings of weighted bipartite planar graphs; t-embeddings also appeared under the name Coulomb gauges in a recent paper arXiv:1810.05616. We argue that this framework is…
The general construction of lattice (co)homology assigns to a lattice $\mathbb{Z}^r$ and a weight function $w:\mathbb{Z}^r \to \mathbb{Z}$ a bigraded $\mathbb{Z}[U]$-module $\mathbb{H}_*$. The weight function $w$ is often obtained from some…
We introduce a very natural topology on the set of total orderings of monomials of any algebra having a countable basis over a field. This topological space and some notable subspaces are compact. This topological framework allows us to…
In the first of the series of papers devoted to our project ``Holomorphic Floer Theory" we discuss exponential integrals and related wall-crossing structures. We emphasize two points of view on the subject: the one based on the ideas of…
This paper studies the combinatorics of ideals which recently appeared in ergodicity results for analytic equivalence relations. The ideals have the following topological representation. There is a separable metrizable space $X$, a…
We prove that the Hitchin connection for $\operatorname{SL}_2$ at level four can be understood in terms of the Mumford-Welters connections on bundles of abelian theta functions for Prym torsors of all unramified double covers, and use this…
The first part of this paper is a survey on algebro-geometric aspects of sheaves of logarithmic vector fields of hyperplane arrangements. In the second part we prove that the relative de Rham cohomology (of degree two) of ADE-type adjoint…
It is shown that the derived dimension of any representation-finite Artin algebra is at most one.