The Rasmussen invariant of a homogeneous knot

Abe, Tetsuya

doi:10.1090/S0002-9939-2010-10687-1

The Rasmussen invariant of a homogeneous knot
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by Tetsuya Abe PDF

Proc. Amer. Math. Soc. 139 (2011), 2647-2656 Request permission

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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