Related papers: Two isomorphism criteria for directed colimits

This paper is a sequel of arXiv:2109.06394. In this paper, we consider a kind of inverse problem of multipliers. The problem is to count number of isospectral correspondences, correspondences which has the same combination of multipliers.…

It was shown by Gersten that a central extension of a finitely generated group is quasi-isometrically trivial provided that its Euler class is bounded. We say that a finitely generated group $G$ satisfies Property QITB (quasi-isometrically…

We show that any collection of n-dimensional orbifolds with sectional curvature and volume uniformly bounded below, diameter bounded above, and with only isolated singular points contains orbifolds of only finitely many orbifold…

Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…

Groupoids are the oidification of groups, and they are largely used in topology and representation theory. We consider here the category $\mathsf{Gpd}$ of all groupoids with all morphisms, and the category $\mathsf{Gpd}_\Lambda$ of…

In contrast to the abundance of "direct" Ramsey results for classes of finite structures (such as finite ordered graphs, finite ordered metric spaces and finite posets with a linear extension), in only a handful of cases we have a…

This paper continues the research of the author on the homology of cubical and semi-cubical sets with coefficients in systems of objects. The main result is the theorem that the homology of cubical sets with coefficients in contravariant…

In a category with enough limits and colimits, one can form the universal automorphism on an endomorphism in two dual senses. Sometimes these dual constructions coincide, as in the categories of finite sets, finite-dimensional vector…

Two finitely generated monoids are constructed, one finitely presented the other not, whose (directed, unlabelled) Cayley graphs are isomorphic.

We fix a finitely presented group $Q$ and consider short exact sequences $1\to N\to G\to Q\to 1$ with $G$ finitely generated. The inclusion $N\to G$ induces a morphism of profinite completions $\hat N\to \hat G$. We prove that this is an…

A uniform approach to computing with infinite objects like real numbers, tuples of these, compacts sets, and uniformly continuous maps is presented. In work of Berger it was shown how to extract certified algorithms working with the signed…

For oriented connected closed manifolds of the same dimension, there is a transitive relation: $M$ dominates $N$, or $M \ge N$, if there exists a continuous map of non-zero degree from $M$ onto $N$. Section 1 is a reminder on the notion of…

Consider a complex projective space with its Fubini-Study metric. We study certain one parameter deformations of this metric on the complement of an arrangement (=a finite union of hyperplanes) whose Levi-Civita connection is of Dunkl…

In 2007, Bogomolov and Tschinkel proved that given two complex elliptic curves $E_1$ and $E_2$ along with even degree-$2$ maps $\pi_j\colon E_j\to \mathbb{P}^1$ having different branch loci, the intersection of the image of the torsion…

We study quantum isometry groups, denoted by $\mathbb{Q}(\Gamma, S)$, of spectral triples on $C^*_r(\Gamma)$ for a finitely generated discrete group coming from the word-length metric with respect to a symmetric generating set $S$. We first…

We study the complexity of the Graph Isomorphism problem on graph classes that are characterized by a finite number of forbidden induced subgraphs, focusing mostly on the case of two forbidden subgraphs. We show hardness results and develop…

A description is given of those sequences ${\Bbb S}= (S(0),S(1),\dots,S(l))$ of simple modules over a finite dimensional algebra for which there are only finitely many uniserial modules with consecutive composition factors…

In this partly expository paper we compare three different categories of C*-algebras in which crossed-product duality can be formulated, both for actions and for coactions of locally compact groups. In these categories, the isomorphisms…

We prove that algebraic isomorphisms between limit algebras are automatically continuous, and consider consequences of this result. In particular, we give partial solutions to a conjecture of Power [Limit Algebras, Longman, 1992, Notes to…

We investigate extensions of S. Solecki's theorem on closing off finite partial isometries of metric spaces \cite{solecki1} and obtain the following exact equivalence: any action of a discrete group $\Gamma$ by isometries of a metric space…