Year: 2025
Type: article
Abstract: A spatial surface is a compact surface embedded in the [Formula: see text]-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.
Author: Katsunori Arai
Institution: The University of Osaka
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408074446