Helly groups
J Chalopin, V Chepoi, A Genevois, H Hirai… - arXiv preprint arXiv …, 2020 - arxiv.org
Helly graphs are graphs in which every family of pairwise intersecting balls has a non-empty
intersection. This is a classical and widely studied class of graphs. In this article we focus on …
intersection. This is a classical and widely studied class of graphs. In this article we focus on …
Helly meets Garside and Artin
J Huang, D Osajda - Inventiones mathematicae, 2021 - Springer
A graph is Helly if every family of pairwise intersecting combinatorial balls has a nonempty
intersection. We show that weak Garside groups of finite type and FC-type Artin groups are …
intersection. We show that weak Garside groups of finite type and FC-type Artin groups are …
Lattices, injective metrics and the K (π, 1) conjecture
T Haettel - Algebraic & Geometric Topology, 2024 - msp.org
Starting with a lattice with an action of ℤ or ℝ, we build a Helly graph or an injective metric
space. We deduce that the ℓ∞ orthoscheme complex of any bounded graded lattice is …
space. We deduce that the ℓ∞ orthoscheme complex of any bounded graded lattice is …
Computing the nc-rank via discrete convex optimization on CAT (0) spaces
M Hamada, H Hirai - SIAM Journal on Applied Algebra and Geometry, 2021 - SIAM
We study the noncommutative rank (nc-rank) computation of a symbolic matrix whose
entries are linear forms in noncommutative variables. For this problem, polynomial time …
entries are linear forms in noncommutative variables. For this problem, polynomial time …
Cubical-like geometry of quasi-median graphs and applications to geometric group theory
A Genevois - arXiv preprint arXiv:1712.01618, 2017 - arxiv.org
The class of quasi-median graphs is a generalisation of median graphs, or equivalently of
CAT (0) cube complexes. The purpose of this thesis is to introduce these graphs in …
CAT (0) cube complexes. The purpose of this thesis is to introduce these graphs in …
New Garside structures and applications to Artin groups
Garside groups are combinatorial generalizations of braid groups which enjoy many nice
algebraic, geometric, and algorithmic properties. In this article we propose a method for …
algebraic, geometric, and algorithmic properties. In this article we propose a method for …
A link condition for simplicial complexes, and CUB spaces
T Haettel - arXiv preprint arXiv:2211.07857, 2022 - arxiv.org
We motivate the study of metric spaces with a unique convex geodesic bicombing, which we
call CUB spaces. These encompass many classical notions of nonpositive curvature, such …
call CUB spaces. These encompass many classical notions of nonpositive curvature, such …
Old and new challenges in Hadamard spaces
M Bacák - arXiv preprint arXiv:1807.01355, 2018 - arxiv.org
Hadamard spaces have traditionally played important roles in geometry and geometric
group theory. More recently, they have additionally turned out to be a suitable framework for …
group theory. More recently, they have additionally turned out to be a suitable framework for …
Labeled four cycles and the -conjecture for Artin groups
J Huang - Inventiones mathematicae, 2024 - Springer
We show that for a large class of Artin groups with Dynkin diagrams being a tree, the\(K (\pi,
1)\)-conjecture holds. We also establish the\(K (\pi, 1)\)-conjecture for another class of Artin …
1)\)-conjecture holds. We also establish the\(K (\pi, 1)\)-conjecture for another class of Artin …
First-order logic axiomatization of metric graph theory
The main goal of this note is to provide a First-Order Logic with Betweenness (FOLB)
axiomatization of the main classes of graphs occurring in Metric Graph Theory, in analogy to …
axiomatization of the main classes of graphs occurring in Metric Graph Theory, in analogy to …