An Introduction to Virtual Spatial Graph Theory
Thomas Fleming, Blake Mellor
TL;DR
This survey introduces virtual spatial graph theory, unifying spatial graphs and virtual knots, and aims to facilitate further research by summarizing definitions, examples, and known results.
Contribution
It provides a comprehensive overview and unification of virtual spatial graphs, serving as a foundational survey for future developments.
Findings
Definitions and examples of virtual spatial graphs are provided.
Survey of known results in the area is included.
The paper aims to stimulate further research in virtual spatial graph theory.
Abstract
Two natural generalizations of knot theory are the study of spatial graphs and virtual knots. Our goal is to unify these two approaches into the study of virtual spatial graphs. This paper is a survey, and does not contain any new results. We state the definitions, provide some examples, and survey the known results. We hope that this paper will help lead to rapid development of the area.
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Taxonomy
TopicsGeometric and Algebraic Topology · Computational Geometry and Mesh Generation · Homotopy and Cohomology in Algebraic Topology