Structure of geodesics in the Cayley graph of infinite Coxeter groups

• Autorzy: Ryszard Szwarc
• Języki publikacji: EN

Abstrakty

EN

Let (W,S) be a Coxeter system such that no two generators in S commute. Assume that the Cayley graph of (W,S) does not contain adjacent hexagons. Then for any two vertices x and y in the Cayley graph of W and any number k ≤ d = dist(x,y) there are at most two vertices z such that dist(x,z) = k and dist(z,y) = d - k. Allowing adjacent hexagons, but assuming that no three hexagons can be adjacent to each other, we show that the number of such intermediate vertices at a given distance from x and y is at most 3. This means that the group W is hyperbolic in a sense stronger than that of Gromov.

Kategorie tematyczne

• 20F55: Reflection and Coxeter groups
• 20F05: Generators, relations, and presentations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 95
• Numer: 1
• Strony: 79-90

Daty

wydano

2003

Twórcy

autor

Ryszard Szwarc

• Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/cm95-1-7