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

2012/03/20 by Isaac Goldbring, Alessandro Sisto, Goldbring, Isaac +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Logic (math.LO) #math.CO #math.GT #math.LO

paper · pdf · doi:10.48550/arxiv.1203.4609

20 pages, 5 figures. Updated version contains several new results

arxiv created 2012/03/29 · arxiv updated 2012/03/30

Abstract

The end compactification |Γ| of the locally finite graph Γis the union of the graph and its ends, endowed with a suitable topology. We show that π₁(|Γ|) 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, recovering a result of Diestel and Sprüssel.

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