G-Family Polynomials
Sam Nelson, Madeline Brown
TL;DR
This paper introduces new polynomial invariants for G-families of quandles, enhancing the counting invariants for spatial graphs and handlebody-links with proven distinctions from existing invariants.
Contribution
It defines two novel quandle polynomials for G-families and applies them to enhance invariants of spatial graphs and handlebody-links.
Findings
New quandle polynomial invariants for G-families introduced
Enhanced invariants distinguish more spatial graph configurations
Examples demonstrate the effectiveness of the new invariants
Abstract
We introduce two notions of quandle polynomials for G-families of quandles: the quandle polynomial of the associated quandle and a G-family polynomial with coefficients in the group ring of G. As an application we define image subquandle polynomial enhancements of the G-family counting invariant for trivalent spatial graphs and handlebody-links. We provide examples to show that the new enhancements are proper.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry