Coloring invariants of spatial graphs
Maciej Niebrzydowski
TL;DR
This paper introduces new coloring invariants for spatial graphs, including a fundamental quandle and invariants from nonabelian quandle cohomology, enhancing tools for distinguishing spatial graph embeddings.
Contribution
It defines the fundamental quandle for spatial graphs and develops novel invariants based on graph walks and nonabelian quandle cohomology within the category of graph tangles.
Findings
Defined the fundamental quandle for spatial graphs
Developed an invariant based on graph walks
Constructed invariants from nonabelian quandle cohomology
Abstract
We define the fundamental quandle of a spatial graph and several invariants derived from it. In the category of graph tangles, we define an invariant based on the walks in the graph and cocycles from nonabelian quandle cohomology.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Graph Theory Research · Homotopy and Cohomology in Algebraic Topology