Helly groups

DOI10.2140/gt.2025.29.1MaRDI QIDQ6656658

Jérémie Chalopin, Hiroshi Hirai, Anthony Genevois, Damian Osajda, Victor Chepoi

Publication date: 3 January 2025

Published in: Geometry \& Topology (Search for Journal in Brave)

zbMATH Keywords

hyperbolic groupBaum-Connes conjectureinjective spaceCAT(0) cubical groupbiautomaticityHelly groupEZ-boundary

Mathematics Subject Classification ID

Geometric group theory (20F65) Hyperbolic groups and nonpositively curved groups (20F67) Cancellation theory of groups; application of van Kampen diagrams (20F06)

Cites Work

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• A note on \(r\)-dominating cliques
• The geometry of cube complexes and the complexity of their fundamental groups
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• Obstructions to a small hyperbolicity in Helly graphs
• Residually finite non-exact groups
• EZ-structures and topological applications
• Classifying spaces for families of subgroups for systolic groups
• Cubulating small cancellation groups.
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• Artin groups of extra-large type are biautomatic
• Local homology properties of boundaries of groups
• Graphs of some CAT(0) complexes
• On the tight span of an antipodal graph
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• Six theorems about injective metric spaces
• Über iterierte Clique-Graphen
• Small cancellation labellings of some infinite graphs and applications
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• Combinatorics and Geometry of Finite and Infinite Squaregraphs
• Absolute Retracts and Varieties of Reflexive Graphs
• Weakly Modular Graphs and Nonpositive Curvature
• Diameters, centers, and approximating trees of delta-hyperbolicgeodesic spaces and graphs
• Packing and Covering δ-Hyperbolic Spaces by Balls
• Conditions for invariance of set diameters under d-convexification in a graph
• Minimal extensions of graphs to absolute retracts
• Median Algebra
• Collapsible polyhedra and median spaces
• Generosity Helps or an 11-Competitive Algorithm for Three Servers
• Quasi‐median graphs and algebras
• Ends of Group Pairs and Non-Positively Curved Cube Complexes
• On subgroups of R. Thompson's group $ F$ and other diagram groups
• Large‐type Artin groups are systolic
• A coarse Cartan–Hadamard theorem with application to the coarse Baum–Connes conjecture
• Median and injective metric spaces
• The Farrell–Jones conjecture for hyperbolic and CAT(0)-groups revisited
• On the imbedding of systems of compacta in simplicial complexes
• Convexity and fixed-point properties in Helly graphs
• Crystallographic Helly groups

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