A multiple group rack and oriented spatial surfaces
Atsushi Ishii, Shosaku Matsuzaki, Tomo Murao
TL;DR
This paper introduces a new coloring invariant for spatial surfaces embedded in the 3-sphere, using multiple group racks to distinguish different surface types.
Contribution
It develops a novel invariant based on multiple group racks, extending rack theory to classify spatial surfaces.
Findings
Constructed several examples of spatial surfaces.
Defined a coloring invariant using multiple group racks.
Demonstrated the invariant distinguishes different surfaces.
Abstract
A spatial surface is a compact surface embedded in the 3-sphere. In this paper, we provide several typical examples of spatial surfaces and construct a coloring invariant to distinguish them. The coloring is defined by using a multiple group rack, which is a rack version of a multiple conjugation quandle.
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Taxonomy
TopicsGeometric and Algebraic Topology · Computational Geometry and Mesh Generation · Mathematics and Applications