Minimal generating sets of groups of Kim-Manturov

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.

17 pages, to appear in the proceedings of the 14th MSJ-SI, 2024