The Rasmussen invariant of a homogeneous knot

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.

12pages, 6 figures

References in corpus (2)

• Floer homology and knot complements
• State Cycles, Quasipositive Modification, and Constructing H-thick Knots in Khovanov Homology