Self-dual Maps III: projective links
L. Montejano, J. Ramirez Alfonsin, I. Rasskin
TL;DR
This paper provides combinatorial criteria for identifying links in real projective 3-space, exploring their symmetry properties and conditions that distinguish non-alternating projective links.
Contribution
It introduces necessary and sufficient conditions for a link to be projective, connecting antipodal symmetry with combinatorial link properties.
Findings
Characterization of projective links via combinatorial conditions
Relation between antipodal symmetry and link properties
Easy criteria to identify non-alternating projective links
Abstract
In this paper, we present necessary and sufficient combinatorial conditions for a link to be projective, that is, a link in . This characterization is closely related to the notions of antipodally self-dual and antipodally symmetric maps. We also discuss the notion of symmetric cycle, an interesting issue arising in projective links leading us to an easy condition to prevent a projective link to be alternating.
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Taxonomy
TopicsGeometric and Algebraic Topology · Finite Group Theory Research · Advanced Differential Equations and Dynamical Systems