Deep pockets in lattices and other groups

DOI10.1090/S0002-9947-09-04954-XzbMath1269.20034arXivmath/0611575MaRDI QIDQ5189143

Andrew D. Warshall

Publication date: 8 March 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611575

zbMATH Keywords

finitely generated groupsgenerating setshyperbolic groupsinfinite groupsword metricsdead endsdiscrete Heisenberg grouphyperbolic automorphismsfinitely generated Abelian groupsgeodesic wordsdead-end depthsdeep pocketsgroups with regular languages of geodesics

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Hyperbolic groups and nonpositively curved groups (20F67)

Related Items (8)

Connectedness of spheres in Cayley graphs ⋮ Dead ends on wreath products and lamplighter groups ⋮ The rate of escape for random walks on polycyclic and metabelian groups ⋮ Iterated Minkowski sums, horoballs and north-south dynamics ⋮ A group with deep pockets for all finite generating sets. ⋮ Frobenius problem and dead ends in integers ⋮ The curve complex has dead ends ⋮ Finite generating sets of relatively hyperbolic groups and applications to geodesic languages

Cites Work

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• Almost convex groups
• THE UNBOUNDED DEAD-END DEPTH PROPERTY IS NOT A GROUP INVARIANT
• SOME REMARKS ON DEPTH OF DEAD ENDS IN GROUPS
• A finitely presented group with unbounded dead-end depth
• Dead end words in lamplighter groups and other wreath products

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