Construction of non-alternating knots
HTML articles powered by AMS MathViewer
- by Sebastian Baader
- Proc. Amer. Math. Soc. 135 (2007), 2633-2636
- DOI: https://doi.org/10.1090/S0002-9939-07-08904-6
- Published electronically: March 14, 2007
- PDF | Request permission
Abstract:
We investigate the behaviour of Rasmussen’s invariant $s$ under the sharp operation on knots and obtain a lower bound for the sharp unknotting number. This bound leads us to an interesting move that transforms arbitrary knots into non-alternating knots.References
- Daniel Bennequin, Entrelacements et équations de Pfaff, Third Schnepfenried geometry conference, Vol. 1 (Schnepfenried, 1982) Astérisque, vol. 107, Soc. Math. France, Paris, 1983, pp. 87–161 (French). MR 753131
- M. Hedden; Ph. Ording, The Ozsváth-Szabó and Rasmussen concordance invariants are not equal, arXiv: math.GT/0512348, 2005.
- Hitoshi Murakami, Some metrics on classical knots, Math. Ann. 270 (1985), no. 1, 35–45. MR 769605, DOI 10.1007/BF01455526
- J. Rasmussen, Khovanov homology and the slice genus, arXiv: math.GT/0402131, 2004.
- Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288
- Lee Rudolph, Quasipositivity as an obstruction to sliceness, Bull. Amer. Math. Soc. (N.S.) 29 (1993), no. 1, 51–59. MR 1193540, DOI 10.1090/S0273-0979-1993-00397-5
- A. Shumakovitch, Rasmussen invariant, slice-Bennequin inequality, and sliceness of knots, arXiv: math.GT/0411643, 2004.
Bibliographic Information
- Sebastian Baader
- Affiliation: Mathematisches Institut, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
- MR Author ID: 757518
- Email: sebastian.baader@math.ethz.ch
- Received by editor(s): March 6, 2006
- Published electronically: March 14, 2007
- Communicated by: Daniel Ruberman
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 2633-2636
- MSC (2000): Primary 57M27
- DOI: https://doi.org/10.1090/S0002-9939-07-08904-6
- MathSciNet review: 2302586