English

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.

Keywords

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