On Invariants of Morse Knots
Geometric Topology
2007-05-23 v1
Abstract
We define and study Vassiliev invariants for (long) Morse knots. It is shown that there are Vassiliev invariants which can distinguish some topologically equivalent Morse knots. In particular, there is an invariant of order 3 for Morse knots with one maximum that distinguishes two different representations of the figure eight knot. We also present the results of computer calculations for some invariants of low order. It turns out that for Morse knots with two maxima there is a Z/2-valued invariant of order 6 which is not a reduction of any integer-valued invariant.
Keywords
Cite
@article{arxiv.math/0008096,
title = {On Invariants of Morse Knots},
author = {Jacob Mostovoy and Theodore Stanford},
journal= {arXiv preprint arXiv:math/0008096},
year = {2007}
}
Comments
12 pages, lots of figures