Triangle Topology Seminar
Monday, September 30, 2019, 3:15pm, 119 Physics
Caitlin Leverson (Georgia Tech)
DGA Representations, Ruling Polynomials, and the Colored HOMFLY-PT Polynomial
Abstract:- Given a pattern braid $\beta\in J^1(S^1)$, to any Legendrian knot $\Lambda$ in $\mathbb{R}^3$ with the standard contact structure, we can associate the Legendrian satellite knot $S(\Lambda,\beta)$. We will discuss the relationship between counts of augmentations of the ChekanovEliashberg differential graded algebra of $S(\Lambda,\beta)$ and counts of certain representations of the algebra of $\Lambda$. We will then define an $m$graded $n$colored ruling polynomial from the $m$graded ruling polynomial, analogously to how the $n$colored HOMFLYPT polynomial is
defined from the HOMFLYPT polynomial, and extend results of the second author, to show that the $2$graded $n$colored ruling polynomial appears as a specialization of the $n$colored HOMFLYPT polynomial. This is joint work with Dan Rutherford.
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