23 citations · 100 across the 31 of their papers we have counts for
37 papers · 1 filter
Composition Properties of Hyperbolic Links in Handlebodies
Colin Adams, Daniel Santiago
We consider knots and links in handlebodies that have hyperbolic complements and operations akin to composition. Cutting the complements of two such open along separating twice-pun…
Hyperbolic Knotoids
Colin Adams, Alexandra Bonat, Maya Chande +6
In 2010, Turaev introduced knotoids as a variation on knots that replaces the embedding of a circle with the embedding of a closed interval with two endpoints. A variety of knot in…
Generalizations of Knotoids and Spatial Graphs
Colin Adams, Alexandra Bonat, Maya Chande +6
In 2010, Turaev introduced knotoids as a variation on knots that replaces the embedding of a circle with the embedding of a closed interval with two endpoints which here we call po…
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…
Virtual Multicrossings and Petal Diagrams for Virtual Knots and Links
Colin Adams, Chaim Even-Zohar, Jonah Greenberg +6
Multicrossings, which have previously been defined for classical knots and links, are extended to virtual knots and links. In particular, petal diagrams are shown to exist for all…
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 .
Modifications Preserving Hyperbolicity of Link Complements
Colin Adams, William H. Meeks, Álvaro K. Ramos
Given a link in a 3-manifold such that the complement is hyperbolic, we provide two modifications to the link, called the chain move and the switch move, that preserve hyperbolicit…
Turaev Hyperbolicity of Classical and Virtual Knots
Colin Adams, Or Eisenberg, Jonah Greenberg +5
By work of W. Thurston, knots and links in the 3-sphere are known to either be torus links, or to contain an essential torus in their complement, or to be hyperbolic, in which case…
Knot Theory for Proteins: Gauss Codes, Quandles and Bondles
Colin Adams, Judah Devadoss, Mohamed Elhamdadi +1
Proteins are linear molecular chains that often fold to function. The topology of folding is widely believed to define its properties and function, and knot theory has been applied…
TG-Hyperbolicity of Virtual Links
Colin Adams, Or Eisenberg, Jonah Greenberg +5
We extend the theory of hyperbolicity of links in the 3-sphere to tg-hyperbolicity of virtual links, using the fact that the theory of virtual links can be translated into the theo…
Hyperbolicity of Links in Thickened Surfaces
Colin Adams, Carlos Albors-Riera, Beatrix Haddock +3
Menasco showed that a non-split, prime, alternating link that is not a 2-braid is hyperbolic in . We prove a similar result for links in closed thickened surfaces …
Generalized bipyramids and hyperbolic volumes of alternating -uniform tiling links
Colin Adams, Aaron Calderon, Nathaniel Mayer
We present explicit geometric decompositions of the hyperbolic complements of alternating -uniform tiling links, which are alternating links whose projection graphs are -unif…
Triple-crossing number and moves on triple-crossing link diagrams
Colin Adams, Jim Hoste, Martin Palmer
Every link in the 3-sphere has a projection to the plane where the only singularities are pairwise transverse triple points. The associated diagram, with height information at each…
Waist size for cusps in hyperbolic 3-manifolds II
Colin Adams
The waist size of a cusp in an orientable hyperbolic 3-manifold is the length of the shortest nontrivial curve generated by a parabolic isometry in the maximal cusp boundary. Previ…
Densities of Hyperbolic Cusp Invariants
Colin Adams, Rose Kaplan-Kelly, Michael Moore +3
We find that cusp densities of hyperbolic knots in the 3-sphere are dense in [0,0.6826...] and those of links are dense in [0,0.853...]. We define a new invariant associated with c…
Bipyramid Decompositions of Multi-crossing Link Complements
Colin Adams, Gregory Kehne
Generalizing previous constructions, we present a dual pair of decompositions of the complement of a link L into bipyramids, given any multi-crossing projection of L. When L is hyp…
Generalized bipyramids and hyperbolic volumes of tiling links
Colin Adams, Aaron Calderon, Xinyi Jiang +4
We present explicit geometric decompositions of the complement of tiling links, which are alternating links whose projection graphs are uniform tilings of the 2-sphere, the Euclide…
Bipyramids and bounds on volumes of hyperbolic links
Colin Adams
We utilize ideal bipyramids to obtain new upper bounds on volume for hyperbolic link complements in terms of the combinatorics of their projections.
Volume and Determinant Densities of Hyperbolic Rational Links
Colin Adams, Aaron Calderon, Xinyi Jiang +4
The volume density of a hyperbolic link is defined as the ratio of hyperbolic volume to crossing number. We study its properties and a closely-related invariant called the determin…
Generalized augmented alternating links and hyperbolic volume
Colin Adams
Augmented alternating links are links obtained by adding trivial components that bound twice-punctured disks to non-split reduced non-2-braid prime alternating projections. These l…
Multi-crossing Number for Knots and the Kauffman Bracket Polynomial
Colin Adams, Orsola Capovilla-Searle, Jesse Freeman +5
A multi-crossing (or n-crossing) is a singular point in a projection at which n strands cross so that each strand bisects the crossing. We generalize the classic result of Kauffman…
Bounds on Übercrossing and Petal Numbers for Knots
Colin Adams, Orsola Capovilla-Searle, Jesse Freeman +5
An -crossing is a point in the projection of a knot where strands cross so that each strand bisects the crossing. An übercrossing projection has a single -crossing and a…
Quadruple crossing number of knots and links
Colin Adams
A quadruple crossing is a crossing in a projection of a knot or link that has four strands of the knot passing straight through it. A quadruple crossing projection is a projection…