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Cocycle Invariants and Oriented Singular Knots
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Mediterranean Journal of Mathematics
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2021-09-07
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18
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5
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Abstract
We extend the quandle cocycle invariant to oriented singular knots and links using algebraic structures called oriented singquandles and assigning weight functions at both regular and singular crossings. This invariant coincides with the classical cocycle invariant for classical knots, but provides extra information about singular knots and links. The new invariant distinguishes the singular granny knot from the singular square knot.
Citation
Ceniceros, J., Churchill, I.R., Elhamdadi, M. et al. Cocycle Invariants and Oriented Singular Knots. Mediterr. J. Math. 18, 217 (2021). https://doi.org/10.1007/s00009-021-01867-6
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This version of the article has been accepted for publication, after peer review (when applicable) but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00009-021-01867-6. Use of this Accepted Version is subject to the publisher’s Accepted Manuscript terms of use https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms’