Minimal generating sets of groups of Kim-Manturov

Takuya Sakasai; Yuuki Tadokoro; Kokoro Tanaka

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arXiv · 2506.05778

Minimal generating sets of groups of Kim-Manturov

Takuya Sakasai·Yuuki Tadokoro·Kokoro Tanaka

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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.

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Takuya Sakasai, Yuuki Tadokoro, Kokoro Tanaka. 2025-06-06. Minimal generating sets of groups of Kim-Manturov. https://arxiv.org/abs/2506.05778

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