For every Legendrian knot, ungraded n-dimensional representation numbers of its contact homology DGA equal the n-colored Kauffman polynomial specialized at a^{-1}=0.
A skein approach to Bennequin type inequalities
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abstract
We give a simple unified proof for several disparate bounds on Thurston-Bennequin number for Legendrian knots and self-linking number for transverse knots in R^3, and provide a template for possible future bounds. As an application, we give sufficient conditions for some of these bounds to be sharp.
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2019 1verdicts
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Legendrian DGA Representations and the Colored Kauffman Polynomial
For every Legendrian knot, ungraded n-dimensional representation numbers of its contact homology DGA equal the n-colored Kauffman polynomial specialized at a^{-1}=0.