# Topology of finite graphs

```@article{Stallings1983TopologyOF,
title={Topology of finite graphs},
author={John R. Stallings},
journal={Inventiones mathematicae},
year={1983},
volume={71},
pages={551-565}
}```
• J. Stallings
• Published 1 March 1983
• Mathematics
• Inventiones mathematicae
This paper derives from a course in group theory which I gave at Berkeley in 1982. I wanted to prove the standard theorems on free groups, and discovered that, after a few preliminaries, the notion of "locally injective" map (or "immersion") of graphs was very useful. This enables one to see, in an effective, easy, algorithmic way just what happens with finitely generated free groups. One can understand in this way (1) Howson's theorem that if A and B are finitely generated subgroups of a free…
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