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Cocycle Enhancements of Psyquandle Counting Invariants

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arxiv 2009.14802 v1 pith:UZUDALQU submitted 2020-09-30 math.GT math.QA

Cocycle Enhancements of Psyquandle Counting Invariants

Jose Ceniceros , Sam Nelson This is my paper
classification math.GT math.QA
keywords cocycleenhancementscountinginvariantsbiquandledefineinvariantpolynomial
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We bring cocycle enhancement theory to the case of psyquandles. Analogously to our previous work on virtual biquandle cocycle enhancements, we define enhancements of the psyquandle counting invariant via pairs of a biquandle 2-cocycle and a new function satisfying some conditions. As an application we define new single-variable and two-variable polynomial invariants of oriented pseudoknots and singular knots and links. We provide examples to show that the new invariants are proper enhancements of the counting invariant are are not determined by the Jablan polynomial.

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