The Rasmussen invariant of a homogeneous knot
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Abstract:
A homogeneous knot is a generalization of alternating knots and positive knots. We determine the Rasmussen invariant of a homogeneous knot. This is a new class of knots such that the Rasmussen invariant is explicitly described in terms of its diagrams. As a corollary, we obtain some characterizations of a positive knot. In particular, we recover Baader’s theorem which states that a knot is positive if and only if it is homogeneous and strongly quasipositive.References
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Additional Information
- Tetsuya Abe
- Affiliation: Advanced Mathematical Institute, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku Osaka 558-8585, Japan
- Email: t-abe@sci.osaka-cu.ac.jp
- Received by editor(s): March 25, 2010
- Received by editor(s) in revised form: June 22, 2010, and July 8, 2010
- Published electronically: December 20, 2010
- Communicated by: Daniel Ruberman
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2647-2656
- MSC (2010): Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-2010-10687-1
- MathSciNet review: 2784833