Bass-Serre theory for groupoids
Group Theory
2024-03-27 v2 Category Theory
Abstract
In this paper a Bass-Serre theory in the groupoid setting is developed and a structure theorem is established. Any groupoid action without inversion of edges on a forest induces a graph of groupoids, while any graph of groupoids satisfying certain hypothesis admits a canonical associated groupoid, called the fundamental groupoid, and a forest, called the Bass-Serre forest, such that the fundamental groupoid acts on the Bass-Serre forest. The structure theorem states that these processes are mutually inverse.
Cite
@article{arxiv.2107.09576,
title = {Bass-Serre theory for groupoids},
author = {Giulia dal Verme and Thomas Weigel},
journal= {arXiv preprint arXiv:2107.09576},
year = {2024}
}