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ON CONJECTURES ABOUT POSITIVE BRAID KNOTS AND ALMOST ALTERNATING TORUS KNOTS

MARKO STOŠIĆ

Instituto de Sistemas e Robótica and CAMGSD, Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal

https://doi.org/10.1142/S0218216510008509Cited by:0 (Source: Crossref)

Abstract

In this paper we resolve some conjectures concerning positive braid knots and almost alternating torus knots. Namely, we prove that the first Khovanov homology group of positive braid knot is trivial, as conjectured by Khovanov. Also, we generalize this result to show that the same is true in the case of Khovanov–Rozansky homology (sl(n) link homology) for any positive integer n. Moreover, by using the Khovanov homology theory, we prove the classical knot theory conjecture by Adams, that the only almost alternating torus knots are T_{3, 4} and T_{3, 5}.

Keywords:

AMSC: 57M25, 57M27

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