Related papers: Generalized Oxtoby subshifts and hyperfiniteness
It is now very known how the subprojectivity of modules provides a fruitful new unified framework of the classical projectivity and flatness. In this paper, we extend this fact to the category of complexes by generalizing and unifying…
We consider several weaker versions of the notion of conjugacy and orbit equivalence of measure preserving actions of countable groups on probability spaces, involving equivalence of the ultrapower actions and asymptotic intertwining…
Given a finitely generated group $G$ that is relatively finitely presented with respect to a collection of peripheral subgroups, we prove that every infinite subgroup $H$ of $G$ that is bounded in the relative Cayley graph of $G$ is…
We show that there are infinitely many distinct closed classes of colimits (in the sense of the Galois connection induced by commutation of limits and colimits in Set) which are intermediate between the class of pseudo-filtered colimits and…
In this paper, we introduce the classes of weakly surjunctive and linearly surjunctive groups which include all sofic groups and more generally all surjunctive groups. We investigate various properties of such groups and establish in…
In this paper, we introduce a general class of weighted spaces of holomorphic Dirichlet series (with real frequencies) analytic in some half-plane and study composition operators on these spaces. In the particular case when the symbol…
We prove that for every finitely generated hyperbolic group $G$, the action of $G$ on its Gromov boundary induces a hyperfinite equivalence relation.
We prove that any word hyperbolic group which is virtually compact special (in the sense of Haglund and Wise) is conjugacy separable. As a consequence we deduce that all word hyperbolic Coxeter groups and many classical small cancellation…
This paper aims to better understand the link better understand the links between aperiodicity in subshifts and pattern complexity. Our main contribution deals with substitutive subshifts, an equivalent to substitutive tilings in the…
We prove that under fairly general conditions an iterated exchange move gives infinitely many non-conjugate braids. As a consequence, every knot has infinitely many conjugacy classes of n-braid representations if and only if it has one…
We introduce the quasiminimal subshifts, subshifts having only finitely many subsystems. With $\mathbb{N}$-actions, their theory essentially reduces to the theory of minimal systems, but with $\mathbb{Z}$-actions, the class is much larger.…
Recently it was shown that the notion of flow equivalence of shifts of finite type in symbolic dynamics is related to the Morita theory and the Grothendieck group in the theory of Leavitt path algebras \cite{flowa}. In this paper we show…
A systematic method of constructing manifestly supersymmetric $1+1$-dimensional KP Lax hierarchies is presented. Closed expressions for the Lax operators in terms of superfield eigenfunctions are obtained. All hierarchy equations being…
We show that various invariants of a unipotent conjugacy class in a connected semisimple group can be recovered purely in terms of data involving the Weyl group.
This paper studies several aspects of symbolic factors of $\mathcal{S}$-adic subshifts of finite alphabet rank. First, we address a problem raised in [DDPM20] about the topological rank of symbolic factors of $\mathcal{S}$-adic subshifts…
R. Burton and J. Steif developed a strategy to construct examples of strongly irreducible subshifts of finite type admitting several measures of maximal entropy. This strategy exploits a correspondence between equilibrium statistical…
We define canonical subshift of finite type cover for Williams' 1-dimensional generalized solenoids, and use resulting invariants to distinguish some closely related solenoids.
We prove that homotopy invariants of finite degree distinguish homotopy classes of maps of a connected compact CW-complex to a nilpotent connected CW-complex with finitely generated homotopy groups.
We establish a hierarchy of weighted majorization relations for the singularities of generalized Lam\'e equations and the zeros of their Van Vleck and Heine-Stieltjes polynomials as well as for multiparameter spectral polynomials of higher…
In this note, we determine the finite groups whose poset of conjugacy classes of subgroups has breaking points. This leads to a new characterization of the generalized quaternion $2$-groups. A generalization of this property is also…