On Invariants of Morse Knots

Details On Invariants of Morse Knots On Invariants of Morse Knots

2000-08-13

arxiv.org/abs/math/0008096v1

Mathematics

Geometric Topology

12 pages, lots of figures

Scientific paper

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.

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