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 …

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 …

Locally elliptic actions, torsion groups, and nonpositively curved spaces

T Haettel, D Osajda - arXiv preprint arXiv:2110.12431, 2021 - arxiv.org
Extending and unifying a number of well-known conjectures and open questions, we
conjecture that locally elliptic (that is, every element has a bounded orbit) actions by …

Group actions on injective spaces and Helly graphs

T Haettel - arXiv preprint arXiv:2307.00414, 2023 - arxiv.org
These are lecture notes for a minicourse on group actions on injective spaces and Helly
graphs, given at the CRM Montreal in June 2023. We review the basics of injective metric …

Automorphisms and subdivisions of Helly graphs

T Haettel - arXiv preprint arXiv:2307.00401, 2023 - arxiv.org
We study Helly graphs of finite combinatorial dimension, ie whose injective hull is finite-
dimensional. We describe very simple fine simplicial subdivisions of the injective hull of a …

[PDF][PDF] Group actions on injective spaces and Helly graphs Lecture Notes Minicourse at the CRM Montréal, June 2023

T Haettel - arXiv preprint arXiv:2307.00414, 2023 - imag.umontpellier.fr
Injective metric spaces and Helly graphs have recently become a very active object of study
in geometric group theory, intiated notably by the brilliant article [Lan13] by Lang. Whereas it …