Bilinear Enhancements of Quandle Invariants
| Autor: | Will Gilroy, Sam Nelson |
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| Rok vydání: | 2022 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2206.13377 |
| Popis: | We enhance the quandle counting invariants of oriented classical and virtual knots and links using a construction similar to quandle modules but inspired by symplectic quandle operations rather than Alexander quandle operations. Given a finite quandle $X$ and a vector space $V$ over a field, sets of bilinear forms on $V$ indexed by pairs of elements of $X$ satisfying certain conditions yield new enhanced multiset- and polynomial-valued invariants of oriented classical and virtual knots and links. We provide examples to illustrate the computation of the invariants and to show that the enhancement is proper. Comment: 9 pages. Version 2 includes typo corrections |
| Databáze: | OpenAIRE |
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