On Slavik Jablan's work on 4-moves (Q2827435)
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scientific article; zbMATH DE number 6641130
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Slavik Jablan's work on 4-moves |
scientific article; zbMATH DE number 6641130 |
Statements
19 October 2016
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knot
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link
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Arf invariant
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Burnside problems
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Fox \(n\)-coloring
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Jones polynomial
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Kauffman bracket
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Kawauchi 4-move conjecture
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tangle multiplication
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quartic skein module
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On Slavik Jablan's work on 4-moves (English)
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This paper shows that SnapPy link L12a\(_-\)1388 is reducible to the Hopf link, thus completing the proof that every alternating link of two components and 12 crossings can be reduced to the trivial link or the Hopf link by 4-moves. Along the way, the reader is treated to a trip through the history of this problem (including a Greyhound bus ride from Vancouver to Santa Cruz) and its antecedents. The author notes that an important result of \textit{H. S. M. Coxeter} [in: Proc. fourth Canad. math. Congr. Banff, 1957, 95--122 (1959; Zbl 0093.25003)], ``was not well known and was not listed in Mathematical Reviews''.
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