Quantum Enhancements and Biquandle Brackets
Geometric Topology
2017-02-17 v3 Quantum Algebra
Abstract
We introduce a new class of quantum enhancements we call biquandle brackets, which are customized skein invariants for biquandle colored links.Quantum enhancements of biquandle counting invariants form a class of knot and link invariants that includes biquandle cocycle invariants and skein invariants such as the HOMFLY-PT polynomial as special cases, providing an explicit unification of these apparently unrelated types of invariants. We provide examples demonstrating that the new invariants are not determined by the biquandle counting invariant, the knot quandle, the knot group or the traditional skein invariants.
Keywords
Cite
@article{arxiv.1508.06573,
title = {Quantum Enhancements and Biquandle Brackets},
author = {Sam Nelson and Michael E. Orrison and Veronica Rivera},
journal= {arXiv preprint arXiv:1508.06573},
year = {2017}
}
Comments
19 pages. New examples added,typos corrected. To appear in J. Knot Theory Ramifications