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Preprint Number 436

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436. Isaac Goldbring, Alessandro Sisto
The fundamental group of a locally finite graph with ends: a hyperfinite approach
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Submission date: 4 April 2012

Abstract:

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 Sprüssel.

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Full text arXiv 1203.4609: pdf, ps.


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