TY - JOUR

T1 - Big subsets with small boundaries in a graph with a vertex-transitive group of automorphisms

AU - Seifter, Norbert

AU - Trofimov, Vladimir I.

PY - 2017/12/2

Y1 - 2017/12/2

N2 - The theory of ends of finitely generated groups $G$ and connected locally finite graphs $\Gamma$ with vertex- transitive groups of automorphisms can be regarded as a theory of Boolean algebras of subsets of $G$ or vertex set of $\Gamma$ with finite boundaries (in the locally finite Cayley graph of $G$ or in $\Gamma$ respectively), considered modulo finite subsets. We develop a more general theory where infinite subsets with finite boundaries are replaced by certain `big' subsets with `small' boundaries.

AB - The theory of ends of finitely generated groups $G$ and connected locally finite graphs $\Gamma$ with vertex- transitive groups of automorphisms can be regarded as a theory of Boolean algebras of subsets of $G$ or vertex set of $\Gamma$ with finite boundaries (in the locally finite Cayley graph of $G$ or in $\Gamma$ respectively), considered modulo finite subsets. We develop a more general theory where infinite subsets with finite boundaries are replaced by certain `big' subsets with `small' boundaries.

KW - graphentheorie

U2 - 10.1070/IM8317

DO - 10.1070/IM8317

M3 - Article

VL - 81.2017

SP - 137

EP - 155

JO - Izvestija Rossijskoj Akademii Nauk. Serija matematičeskaja

JF - Izvestija Rossijskoj Akademii Nauk. Serija matematičeskaja

IS - 1

ER -