On Legendrian knots and polynomial invariants (Q2781267)
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scientific article; zbMATH DE number 1721013
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Legendrian knots and polynomial invariants |
scientific article; zbMATH DE number 1721013 |
Statements
On Legendrian knots and polynomial invariants (English)
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19 March 2002
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contact structures
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Bennequin invariant
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writhe
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Maslov invariant
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slice genus
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HOMFLY polynomial
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Kauffman polynomial
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0.9500953
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0.9455467
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0.9412336
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0.93653905
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0.93463486
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A smooth knot \(l\) embedded in \(\mathbb R^3\) is Legendrian if it is everywhere tangent to the plane field of the standard contact structure on \(\mathbb R^3\). For such a knot the author investigates three inequalities involving the Bennequin invariant (i.e. the negative of the writhe), the Maslov invariant (i.e. the Whitney index), the slice genus, and the least degree of the framing variable \(a\) in the HOMFLY and Kauffman polynomials. He gives a survey of known results, a new proof of one of the inequalities, and examples showing that none of the inequalities is sharp.
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