G-Family Polynomials

Sam Nelson; Madeline Brown

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arXiv · 2103.02710

G-Family Polynomials

Sam Nelson·Madeline Brown

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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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Sam Nelson, Madeline Brown. 2021-03-03. G-Family Polynomials. https://arxiv.org/abs/2103.02710

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