Minimal generating sets of groups of Kim-Manturov
Geometric Topology
2025-06-09 v1
Abstract
We consider a series of groups defined by Kim and Manturov. These groups have their background in triangulations of a surface and configurations of points, lines or circles on the surface. They are expected to have relationships to many geometric objects. In this paper, we give a minimal generating set of the group and determine the abelianization. We also introduce some related groups which might be helpful to understand the structure of the original groups.
Cite
@article{arxiv.2506.05778,
title = {Minimal generating sets of groups of Kim-Manturov},
author = {Takuya Sakasai and Yuuki Tadokoro and Kokoro Tanaka},
journal= {arXiv preprint arXiv:2506.05778},
year = {2025}
}
Comments
17 pages, to appear in the proceedings of the 14th MSJ-SI, 2024