Open Access
April 2015 Isotopy and homotopy invariants of classical and virtual pseudoknots
François Dorais, Allison Henrich, Slavik Jablan, Inga Johnson
Osaka J. Math. 52(2): 409-423 (April 2015).


Pseudodiagrams are knot or link diagrams where some of the crossing information is missing. Pseudoknots are equivalence classes of pseudodiagrams, where equivalence is generated by a natural set of Reidemeister moves. In this paper, we introduce a Gauss-diagrammatic theory for pseudoknots which gives rise to the notion of a virtual pseudoknot. We provide new, easily computable isotopy and homotopy invariants for classical and virtual pseudodiagrams. We also give tables of unknotting numbers for homotopically trivial pseudoknots and homotopy classes of homotopically nontrivial pseudoknots. Since pseudoknots are closely related to singular knots, this work also has implications for the classification of classical and virtual singular knots.


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François Dorais. Allison Henrich. Slavik Jablan. Inga Johnson. "Isotopy and homotopy invariants of classical and virtual pseudoknots." Osaka J. Math. 52 (2) 409 - 423, April 2015.


Published: April 2015
First available in Project Euclid: 24 March 2015

zbMATH: 1365.57013
MathSciNet: MR3326618

Primary: 57M27

Rights: Copyright © 2015 Osaka University and Osaka City University, Departments of Mathematics

Vol.52 • No. 2 • April 2015
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