arXiv subjects

Martín Blufstein

Publications and source records attributed to Martín Blufstein.

8 recordsLinked to original sources

arXiv2026

Assouad--Nagata dimension of systolic complexes with almost flat intervals

We introduce the notion of systolic complexes with almost flat intervals. They constitute a subclass of fit systolic complexes and arise naturally in the study of graphical C(3)--T(6) small cancellation complexes. We prove that their Assouad--Nagata dimension is bounded above by a universal constant. As consequences, we obtain universal bounds on the Assouad--Nagata dimension of tame simply connected graphical C(3)--T(6) small cancellation complexes and of finitely generated groups defined by graphical C(3)--T(6) small cancellation presentations. In the appendix, we observe that the proof of finiteness of asymptotic dimension for buildings due to Dymara and Schick also yields finiteness of their asymptotic Assouad--Nagata dimension.

math.GR↗

arXiv2026

Helly complexes are Hellyfications of their boundaries

We prove that every finite Helly complex is isomorphic, at the level of its $1$-skeleton, to the Hellyfication (equivalently, the discrete injective hull) of its combinatorial boundary equipped with the metric induced from the complex. In particular, the boundary-rigidity phenomenon for Helly complexes proved by Blufstein-Chalopin-Chepoi admits a canonical injective-hull interpretation, independent of reconstruction procedures based on dismantling.

math.CO↗

arXiv2026

Fit systolic groups, exactly

A systolic complex/bridged graph is fit when its (metric) intervals are "not too large". We prove that uniformly locally finite fit systolic complexes have Yu's Property A. In particular, groups acting properly on such complexes have Property A, (equivalently) they are exact, and (equivalently) they are boundary amenable. As applications we show that groups from a class containing all large-type Artin groups, as well as all finitely presented graphical $C(3)$--$T(6)$ small cancellation groups, and finitely presented classical $C(6)$ small cancellation groups are exact. We also provide further examples. Our proof relies on a combinatorial criterion for Property~A due to Špakula and Wright.

math.GR↗

arXiv2026

Boundary rigidity of systolic and Helly complexes

In this article, we prove that finite (weakly) systolic and Helly complexes can be reconstructed from their boundary distances (computed in their 1-skeleta). Furthermore, Helly complexes and 2-dimensional systolic complexes can be reconstructed by an algorithm that runs in polynomial time with respect to the number of vertices of the complex. Both results can be viewed as a positive contribution to a general question of Haslegrave, Scott, Tamitegama, and Tan (2025). The reconstruction of a finite cell complex from the boundary distances is the discrete analogue of the boundary rigidity problem, which is a classical problem from Riemannian geometry.

math.CO↗

arXiv2025

Strong solidity classification of Coxeter groups

We prove the dichotomy that every Coxeter group either has a strongly solid group von Neumann algebra or contains the product of an infinite cyclic group and a free group of rank 2. This generalizes the same dichotomy for right-angled Coxeter groups by Borst-Caspers. However, our proof is conceptually different, which leads to a significantly streamlined argument. We also provide additional equivalent geometric and group-theoretic characterizations of strong solidity for Coxeter groups that allow us to completely classify those with a strongly solid group von Neumann algebra. In particular, we characterize strong solidity purely in terms of the defining Coxeter-Dynkin diagram. Finally, we obtain the same dichotomy for virtually cocompact special groups.

math.OA↗

arXiv2025

On the twisted conjugacy problem for large-type Artin groups

We show that the twisted conjugacy problem is solvable for large-type Artin groups whose outer automorphism group is finite, generated by graph automorphisms and the global inversion. This includes XXXL Artin groups whose defining graph is connected, twistless, and not an even edge; and large-type Artin groups whose defining graph admits a twistless hierarchy terminating in twistless stars.

math.GR↗

arXiv2025

Homomorphisms between XL-type Artin groups

We study homomorphisms between XL-type Artin groups and show that, in a suitable sense, a generic Artin group is both hopfian and co-hopfian. For XL-type Artin groups over complete graphs, we describe all possible homomorphisms with sufficiently large image, and prove in particular that such groups are both hopfian and co-hopfian. For Artin groups over general graphs with all labels at least $6$, we characterise in terms of the presentation graph exactly when these groups are co-hopfian, as well as when they have a finite outer automorphism group. When in addition the presentation graph has no cut-vertex, we show that their automorphism group is finitely generated and we provide a generating set.

math.GR↗

arXiv2024

When is a TRAAG orderable?

We characterize, in terms of the defining graph, when a twisted right-angled Artin group (a group whose only relations among pairs of generators are either commuting or Klein-bottle type relations) is left-orderable.

math.GR↗