50 citations · 169 across the 22 of their papers we have counts for
22 papers
Skein relations for invariants of Legendrian surfaces
Dan Rutherford, Michael G. Sullivan
For Legendrian surfaces in 1-jet spaces, we consider augmentation number invariants that together generalize the ruling polynomial of 1-dimensional Legendrian knots and establish s…
Augmented Legendrian cobordism in
Yu Pan, Dan Rutherford
We consider Legendrian links and tangles in and equipped with Morse complex families over a field and classify them up to Legendrian cobordism. Whe…
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…
Augmentations and immersed Lagrangian fillings
Yu Pan, Dan Rutherford
For a Legendrian link with or , immersed exact Lagrangian fillings $L \subset \mbox{Symp}(J^1M) \cong T^*(\mathbb{R}_{>0} \times M)$ of ca…
Sheaves via augmentations of Legendrian surfaces
Dan Rutherford, Michael G. Sullivan
Given an augmentation for a Legendrian surface in a -jet space, , we explicitly construct an object, , of the (derived) category from arXi…
Legendrian DGA Representations and the Colored Kauffman Polynomial
Justin Murray, Dan Rutherford
For any Legendrian knot in standard contact we relate counts of ungraded (-graded) representations of the Legendrian contact homology DG-algebra $(\mathcal{A…