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

Norbert Seifter, Vladimir I. Trofimov

Research output: Contribution to journalArticleResearchpeer-review


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.
Original languageEnglish
Pages (from-to)137-155
Number of pages19
JournalIzvestija Rossijskoj Akademii Nauk. Serija matematičeskaja
Issue number1
Publication statusPublished - 2 Dec 2017

Cite this