The Rasmussen invariant of a homogeneous knot
Geometric Topology
2010-03-30 v1
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.
Cite
@article{arxiv.1003.5392,
title = {The Rasmussen invariant of a homogeneous knot},
author = {Tetsuya Abe},
journal= {arXiv preprint arXiv:1003.5392},
year = {2010}
}
Comments
12pages, 6 figures