3 citations · 3 across the 4 of their papers we have counts for
5 papers
Vanishing of higher Legendrian homology for rainbow closures
Roger Casals, Alexander Simons
We show that the higher Legendrian homology of any Legendrian link given by the rainbow closure of a positive braid must necessarily vanish. The result is proven in the most genera…
Lower Bounds on Volumes of Hyperbolic 3-Manifolds via Decomposition
Colin Adams, Michele Capovilla-Searle, Darin Li +5
In a variety of settings we provide a method for decomposing a 3-manifold into pieces. When the pieces have the appropriate type of hyperbolicity, then the manifold is hype…
TG-Hyperbolicity of Composition of Virtual Knots
Colin Adams, Alexander Simons
The composition of any two nontrivial classical knots is a satellite knot, and thus, by work of Thurston, is not hyperbolic. In this paper, we explore the composition of virtual kn…
Generalized Augmented Cellular Alternating Links in Thickened Surfaces are Hyperbolic
Colin Adams, Michele Capovilla-Searle, Darin Li +5
Menasco proved that nontrivial links in the 3-sphere with connected prime alternating non-2-braid projections are hyperbolic. This was further extended to augmented alternating lin…
Superbridge and Bridge Indices for Knots
Colin Adams, Nikhil Agarwal, Rachel Allen +4
We improve the upper bound on the superbridge index of a knot type in terms of the bridge index from to .