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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Rasmussen invariant of a homogeneous knot


Author: Tetsuya Abe
Journal: Proc. Amer. Math. Soc. 139 (2011), 2647-2656
MSC (2010): Primary 57M25
Published electronically: December 20, 2010
MathSciNet review: 2784833
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10687-1
PII: S 0002-9939(2010)10687-1
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.