The Rasmussen invariant of a homogeneous knot

Tetsuya Abe

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arXiv · 1003.5392

The Rasmussen invariant of a homogeneous knot

Tetsuya Abe

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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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Tetsuya Abe. 2010-03-28. The Rasmussen invariant of a homogeneous knot. https://arxiv.org/abs/1003.5392

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