Open Access
March 2012 Knotoids
Vladimir Turaev
Osaka J. Math. 49(1): 195-223 (March 2012).


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 $S^{2}$ generalize knots in $S^{3}$ and study the semigroup of knotoids. We also discuss applications to knots and invariants of knotoids.


Download Citation

Vladimir Turaev. "Knotoids." Osaka J. Math. 49 (1) 195 - 223, March 2012.


Published: March 2012
First available in Project Euclid: 21 March 2012

zbMATH: 1271.57030
MathSciNet: MR2919689

Primary: 57M25 , 57M27

Rights: Copyright © 2012 Osaka University and Osaka City University, Departments of Mathematics

Vol.49 • No. 1 • March 2012
Back to Top