Reinhard Diestel, Philipp Sprüssel
The Fundamental Group of Locally Finite Graphs with Ends
Preprint series: ESI preprints

MSC:

05C10 Topological graph theory, imbedding, See also {57M15, 57M25}

05C25 Graphs and groups, See also {20F32}

57M05 Fundamental group, presentations, free differential calculus

57M15 Relations with graph theory, See also {05Cxx}

Abstract: We characterize the fundamental group of a locally finite graph $G$ with ends, by embedding it
canonically as a subgroup in the inverse limit of the free groups $\pi_1(G')$ with $G'\sub G$ finite.
As an intermediate step, we characterize $\pi_1(|G|)$ combinatorially as a group of infinite words.


Keywords: infinite graphs, ends of graphs, topological graph theory, fundamental group