Counterexamples to Kauffman's conjectures on slice knots
| Autor: | Christopher William Davis, Tim D. Cochran |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Knot complement
General Mathematics Quantum invariant 010102 general mathematics Skein relation Geometric Topology (math.GT) Tricolorability Mathematics::Geometric Topology 01 natural sciences Knot theory 010101 applied mathematics Combinatorics Mathematics - Geometric Topology Seifert surface Knot invariant 57M25 FOS: Mathematics Slice knot 0101 mathematics Mathematics |
| Zdroj: | Advances in Mathematics. 274:263-284 |
| ISSN: | 0001-8708 |
| DOI: | 10.1016/j.aim.2014.12.006 |
| Popis: | In 1982 Louis Kauffman conjectured that if a knot in the 3-sphere is a slice knot then on any Seifert surface for that knot there exists a homologically essential simple closed curve of self-linking zero which is itself a slice knot, or at least has Arf invariant zero. Since that time, considerable evidence has been amassed in support of this conjecture. In particular, many invariants that obstruct a knot from being a slice knot have been explictly expressed in terms of invariants of such curves on the Seifert surface. We give counterexamples to Kauffman's conjecture, that is, we exhibit (smoothly) slice knots that admit (unique minimal genus) Seifert surfaces on which every homologically essential simple closed curve of self-linking zero has non-zero Arf invariant and non-zero signatures. 17 pages, 11 Figures, minor corrections/clarifications and up-dated references in version 2 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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