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19 April 2024 |
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Isotopy and Homotopy Invariants of Classical and Virtual Pseudoknots | | Francois Dorais
; Allison Henrich
; Slavik Jablan
; Inga Johnson
; | | Date: |
14 Nov 2013 | | Abstract: | 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. | | Source: | arXiv, 1311.3658 | | Services: | Forum | Review | PDF | Favorites | |
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