On invariants of Morse knots
| Autor: | Jacob Mostovoy, Theodore Stanford |
|---|---|
| Rok vydání: | 2002 |
| Předmět: |
Vassiliev invariants
Morse knots Skein relation Figure-eight knot Geometric Topology (math.GT) Morse code Mathematics::Geometric Topology Finite type invariant law.invention Knot theory Combinatorics Mathematics - Geometric Topology law 57M27 57M25 FOS: Mathematics Geometry and Topology Invariant (mathematics) Topological conjugacy Circle-valued Morse theory Mathematics |
| Zdroj: | Topology and its Applications. 121(1-2):105-118 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/s0166-8641(01)00113-4 |
| Popis: | 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. 12 pages, lots of figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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