Related papers: One-sided Hom shifts

We survey some topics in ${\mathbb A}^1$-homotopy theory. Our main goal is to highlight the interplay between ${\mathbb A}^1$-homotopy theory and affine algebraic geometry, focusing on the varieties that are "contractible" from various…

We study tree-to-tree transformations that can be defined in first-order logic or monadic second-order logic. We prove a decomposition theorem, which shows that every transformation can be obtained from prime transformations, such as…

The string group acts on the category of coherent sheaves over a weighted projective line by degree-shift actions. We study the equivariant equivalence relations induced by degree-shift actions between weighted projective lines. We prove…

We consider the set of H\"older continuous cocycles over a finite shift acting on a group of Lipschitz homeomorphisms Lip(G), where G is a metrisable compact topological group. We establish that two dominated cocycles that coincide over…

Uniformly finite homology is a coarse invariant for metric spaces; in particular, it is a quasi-isometry invariant for finitely generated groups. In this article, we study uniformly finite homology of finitely generated amenable groups and…

We prove that a smooth scheme of dimension $n$ over a perfect field is A^1-weakly equivalent to a point if it is A^1-n-connected. We also prove an excision result for A^1-homotopy sheaves over a perfect field.

The dominating graph of a graph $H$ has as its vertices all dominating sets of $H$, with an edge between two dominating sets if one can be obtained from the other by the addition or deletion of a single vertex of $H$. In this paper we prove…

We investigate here the hardness of conjugacy and factorization of subshifts of finite type (SFTs) in dimension $d>1$. In particular, we prove that the factorization problem is $\Sigma^0_3$-complete and the conjugacy problem…

We address the following open problem, implicit in the 1990 article "Automorphisms of one-sided subshifts of finite type" of Boyle, Franks and Kitchens (BFK): "Does there exists an element $\psi$ in the group of automorphisms of the…

We describe structural properties of strongly connected finite directed graphs, that are invariants of the topological conjugacy of their Markov-Dyck shifts. For strongly connected finite directed graphs with these properties topological…

In this note we prove that the constant and equivariant cyclic cohomology of algebras coincide. This shows that constant cyclic cohomology is rich and computable.

We investigate what happens when we try to work with continuing block codes (i.e. left or right continuing factor maps) between shift spaces that may not be shifts of finite type. For example, we demonstrate that continuing block codes on…

A matching complex of a simple graph $G$ is a simplicial complex with faces given by the matchings of $G$. The topology of matching complexes is mysterious; there are few graphs for which the homotopy type is known. Marietti and Testa…

The degree of mixing is a fundamental property of a dynamical system. General multi-dimensional shifts cannot be systematically determined. This work introduces constructive and systematic methods for verifying the degree of mixing, from…

We prove some new properties of fidelity (transition probability) and concurrence, the latter defined by straightforward extension of Wootters notation. Choose a conjugation and consider the dependence of fidelity or of concurrence on…

In this paper we initiate the study of the forward and backward shifts on the Hardy space of a tree and the little Hardy space of a tree. In particular, we investigate when these shifts are bounded, find the norm of the shifts if they are…

We prove certain conjecture holds true for a finite category which has M\"obius inversion. The conjecture states a relationship between the zeta function of a finite category and the Euler characteristic of a finite category.

A hom-associative structure is a set $A$ together with a binary operation $\star$ and a selfmap $\alpha$ such that an $\alpha$-twisted version of associativity is fulfilled. In this paper, we assume that $\alpha$ is surjective. We show that…

The authors conjectured previously that a knot is nonfibered if and only if its infinite cyclic cover has uncountably many finite covers. We prove the conjecture for a class of knots that includes all knots of genus 1, using techniques from…

We prove a fix point theorem for monoids of self-embeddings of trees. As a corollary, we obtain a result by Laflamme, Pouzet and Sauer that a tree either contains a subdivided binary tree as a subtree or has a vertex, and edge, an end or…