Vertex links and the Grushko decomposition
Group Theory
2023-10-24 v2 Geometric Topology
Abstract
We develop an algorithm of polynomial time complexity to construct the Grushko decomposition of fundamental groups of graphs of free groups with cyclic edge groups. Our methods rely on analysing vertex links of certain CAT(0) square complexes naturally associated with a special class of the above groups. Our main result transforms a one-ended CAT(0) square complex of the above type to one whose vertex links satisfy a strong connectivity condition, as first studied by Brady and Meier.
Cite
@article{arxiv.1807.06186,
title = {Vertex links and the Grushko decomposition},
author = {Suraj Krishna M S},
journal= {arXiv preprint arXiv:1807.06186},
year = {2023}
}
Comments
17 pages, 6 figures. v2: Results strengthened. Referee comments incorporated. To appear in Annales de la Facult\'e des Sciences de Toulouse