Proceedings of the American Mathematical Society

Author(s): Sebastian Baader
Journal: Proc. Amer. Math. Soc. 135 (2007), 2633-2636.
MSC (2000): Primary 57M27
Posted: March 14, 2007
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Abstract: We investigate the behaviour of Rasmussen's invariant

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.

1.: D. Bennequin, Entrelacements et équations de Pfaff, Astérisque 107-108 (1982), 87-161. MR 753131 (86e:58070)
2.: M. Hedden; Ph. Ording, The Ozsváth-Szabó and Rasmussen concordance invariants are not equal, arXiv: math.GT/0512348, 2005.
3.: H. Murakami, Some metrics on classical knots, Math. Ann. 270 (1985), no.1, 35-45. MR 769605 (86g:57007)
4.: J. Rasmussen, Khovanov homology and the slice genus, arXiv: math.GT/0402131, 2004.
5.: D. Rolfsen, Knots and Links, Publish or Perish (1976). MR 0515288 (58:24236)
6.: L. Rudolph, Quasipositivity as an obstruction to sliceness, Bull. Amer. Math. Soc. 29 (1993), no.1, 51-59. MR 1193540 (94d:57028)
7.: A. Shumakovitch, Rasmussen invariant, slice-Bennequin inequality, and sliceness of knots, arXiv: math.GT/0411643, 2004.

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 57M27

Sebastian Baader
Affiliation: Mathematisches Institut, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
Email: sebastian.baader@math.ethz.ch

DOI: 10.1090/S0002-9939-07-08904-6
PII: S 0002-9939(07)08904-6
Received by editor(s): March 6, 2006
Posted: March 14, 2007
Communicated by: Daniel Ruberman
Copyright of article: Copyright 2007, American Mathematical Society

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