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The Rasmussen invariant of a homogeneous knot

2010/03/28 by Tetsuya Abe, Abe, Tetsuya
Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25

paper · pdf · doi:10.48550/arxiv.1003.5392

12pages, 6 figures

arxiv created 2010/03/28 · arxiv updated 2010/03/30

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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