Dan Rutherford

activity

20052021

most citedSheaves via augmentations of Legendrian surfaces

7 citations · 11 across the 3 of their papers we have counts for

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5 papers · 1 filter

math.SG2021

Non-fillable augmentations of twist knots

Honghao Gao, Dan Rutherford

We establish new examples of augmentations of Legendrian twist knots that cannot be induced by orientable Lagrangian fillings. To do so, we use a version of the Seidel-Ekholm-Dimit…

math.SG2019★ 7 cited

Sheaves via augmentations of Legendrian surfaces

Dan Rutherford, Michael G. Sullivan

Given an augmentation for a Legendrian surface in a $1$ -jet space, $Λ \subset J^{1} (M)$ , we explicitly construct an object, $F \in S h_{Λ}$ , of the (derived) category from arXi…

math.SG2019

Legendrian DGA Representations and the Colored Kauffman Polynomial

Justin Murray, Dan Rutherford

For any Legendrian knot $K$ in standard contact $R^{3}$ we relate counts of ungraded ( $1$ -graded) representations of the Legendrian contact homology DG-algebra $(\mathcal{A…

math.SG2019★ 4 cited

Functorial LCH for immersed Lagrangian cobordisms

Yu Pan, Dan Rutherford

For $1$ -dimensional Legendrian submanifolds of $1$ -jet spaces, we extend the functorality of the Legendrian contact homology DG-algebra (DGA) from embedded exact Lagrangian cobordi…

math.SG2018

Satellite ruling polynomials, DGA representations, and the colored HOMFLY-PT polynomial

Caitlin Leverson, Dan Rutherford

We establish relationships between two classes of invariants of Legendrian knots in $R^{3}$ : Representation numbers of the Chekanov-Eliashberg DGA and satellite ruling polyn…