The fundamental group of a locally finite graph with ends - A hyperfinite approach

Isaac Goldbring, Alessandro Sisto

Research output: Contribution to journalArticle

Abstract

The end compactification Λ of a locally finite graph Λ is the union of the graph and its ends, endowed with a suitable topology. We show that π1(Λ) embeds into a nonstandard free group with hyperfinitely many generators, i.e. an ultraproduct of finitely generated free groups, and that the embedding we construct factors through an embedding into an inverse limit of free groups. We also show how to recover the standard description of π1(Λ) given by Diestel and Sprüssel (2011). Finally, we give some applications of our result, including a short proof that certain loops in Λ are non-nullhomologous.

Original languageEnglish
Pages (from-to)21-39
Number of pages19
JournalFundamenta Mathematicae
Volume232
Issue number1
DOIs
Publication statusPublished - 2016

Keywords

  • End compactifiction of a locally finite graph
  • Fundamental group
  • Nonstandard analysis

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'The fundamental group of a locally finite graph with ends - A hyperfinite approach'. Together they form a unique fingerprint.

  • Cite this