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

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

2012-03-20

arxiv.org/abs/1203.4609v2

Mathematics

Geometric Topology

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

Scientific paper

The end compactification |\Gamma| of the locally finite graph \Gamma is the union of the graph and its ends, endowed with a suitable topology. We show that \pi_1(|\Gamma|) 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 Spr\"ussel.

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