The fundamental group of a locally finite graph with ends

2009/10/29 by Reinhard Diestel, Diestel, Reinhard, Philipp Sprüssel +1 · 1 citation
Computer Science · Engineering · Mathematics · #05C63 #14F35 (Primary) 20E18 (Secondary) #Algebraic Topology (math.AT) #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.AT #math.CO #math.GR #msc:05C63 #msc:14F35 #msc:20E18

paper · pdf · doi:10.48550/arxiv.0910.5647

38 pages. This is an extended version of the paper "The fundamental group of a locally finite graph with ends" by the same authors. It differs from that paper only in that it offers proofs for Lemmas 2, 4, 6, 7, 8, 9 and 20, and a longer example in Section 5

arxiv created 2009/10/29 · openalex publication_date 2009/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize the fundamental group of a locally finite graph G with ends combinatorially, as a group of infinite words. Our characterization gives rise to a canonical embedding of this group in the inverse limit of the (free) fundamental groups of the finite subgraphs of G.

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• Locally finite graphs with ends: a topological approach

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