TL;DR
This paper introduces psyquandle brackets, extending biquandle brackets to singular knots and pseudoknots, providing a new family of quantum invariants that can distinguish complex knot types.
Contribution
It develops the theory of quantum enhancements for psyquandle counting invariants, expanding the toolkit for knot invariants beyond existing biquandle-based methods.
Findings
Examples demonstrate the computation of new invariants.
The invariants are proper enhancements, not reducible to previous invariants.
Potential for more powerful invariants with larger psyquandles and coefficient rings.
Abstract
We extend the notion of biquandle brackets to the case of psyquandles, defining quantum enhancements of the psyquandle counting invariant for singular knots and pseudoknots. We provide examples to illustrate the computation of these invariants, establishing that the enhancement is proper. We compute a few toy examples, noting that the true power of this infinite family of invariants lies in more computationally expensive larger-cardinality psyquandles and infinite coefficient rings.
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