The Rasmussen invariant of a homogeneous knot

Details The Rasmussen invariant of a homogeneous knot The Rasmussen invariant of a homogeneous knot

2010-03-28

arxiv.org/abs/1003.5392v1

Mathematics

Geometric Topology

12pages, 6 figures

Scientific paper

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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