Cocycle Invariants and Oriented Singular Knots
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DOI: 10.1007/s00009-021-01867-6
Abstract: We extend the quandle cocycle invariant to oriented singular knots and links using algebraic structures called \emph{oriented singquandles} and assigning weight functions at both regular and singular crossings. This invariant coincides with the classical cocycle… read more here.
Keywords: cocycle invariants; singular knots; invariants oriented; cocycle ... See more keywords
Biquandle cohomology and state-sum invariants of links and surface-links
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Knot Theory and Its Ramifications"
DOI: 10.1142/s0218216518430162
Abstract: In this paper, we discuss the (co)homology theory of biquandles, derived biquandle cocycle invariants for oriented surface-links using broken surface diagrams and how to compute the biquandle cocycle invariants from marked graph diagrams. We also… read more here.
Keywords: state sum; cohomology state; cocycle invariants; surface links ... See more keywords