Seminar za geometriju, obrazovanje i vizualizaciju sa primenama, 4. april 2013.

Naredni sastanak Seminara biće održan u četvrtak, 4. aprila 2013, u 17 časova u sali 301f, MI SANU.

Predavači: Slavik Jablan, Ana Zeković

Naslov predavanja:  The Theory of Pseudoknots and Unknotting Invariants (autori: Slavik Jablan, Ana Zeković, Allison Henrich, Rebecca Hoberg, Lee Johnson, Elizabeth Minten i Ljiljana Radović)

Sadržaj: The Theory of Pseudoknots and Unknotting Invariants Classical knots in R^3 can be represented by diagrams in the plane.  These diagrams are formed by curves with a finite number of transverse  crossings, where each crossing is decorated to indicate which strand of  the knot passes over at that point. A (pseudodiagram) is a knot diagram that may be missing crossing information at some of its crossings. At these crossings, it is undetermined which strand passes  over. Pseudodiagrams were first introduced by Ryo Hanaki in 2010. Here,  we introduce the notion of a pseudoknot, i.e. an equivalence class of  pseudodiagrams under an appropriate choice of Reidemeister moves. In  order to begin a classification of pseudoknots, we introduce the concept  of a weighted resolution set, or WeRe-set, an invariant of pseudoknots.  We compute the WeRe-set for several pseudoknot families and discuss  extensions of crossing number, homotopy, chirality for pseudoknots and  different unknotting invariants connected with pseudoknots and their  homotopy classes.



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