A groupoid rack and spatial surfaces
Geometric Topology
2025-02-25 v5
Abstract
A spatial surface is a compact surface embedded in the -sphere. We assume that a spatial surface is oriented and that each connected component of a spatial surface is neither a disk nor without a boundary. A diagram of a spatial surface is a diagram of a spatial trivalent graph that is a spine of the spatial surface. In this paper, we introduce the notion of a groupoid rack, which is used for considering colorings for diagrams of spatial surfaces in order to obtain an invariant of spatial surfaces. Furthermore, we show that a groupoid rack has a universal property on colorings for diagrams of spatial surfaces.
Cite
@article{arxiv.2310.06423,
title = {A groupoid rack and spatial surfaces},
author = {Katsunori Arai},
journal= {arXiv preprint arXiv:2310.06423},
year = {2025}
}
Comments
19 pages, 13 figures