Swiss Knots 2011

Knot Theory and Algebra

Lake Thun, May 23-27


Prof. Dr. Vladimir Turaev's talk
Date: 24.05.11   Time: 09.00 - 09.50   Room: Gwatt Zentrum

Abstract: We introduce and study knotoids. Knotoids are represented by diagrams in a surface which differ from the usual knot diagrams in that the underlying curve is a segment rather than a circle. Knotoid diagrams are considered up to Reidemeister moves applied away from the endpoints of the underlying segment. We show that knotoids in the 2-sphere generalize knots in the 3-sphere and study the semigroup of knotoids. We also discuss applications to knots and invariants of knotoids.