6 papers · 1 filter
Hyperbolic Knots and Torsion in Khovanov Homology
Micah Chrisman, Sujoy Mukherjee
In this note, we show that if there is a knot in having torsion in its Khovanov homology, then there are infinitely many hyperbolic knots and infinitely many p…
Concordances to prime hyperbolic virtual knots
Micah Chrisman
Let be closed oriented surfaces. Two oriented knots and are said to be (virtually) concordant if there is a…
Virtual Seifert Surfaces
Micah Chrisman
A virtual knot that has a homologically trivial representative in a thickened surface is said to be an almost classical (AC) knot. then…
On the Combinatorics of Smoothing
Micah W. Chrisman
Many invariants of knots rely upon smoothing the knot at its crossings. To compute them, it is necessary to know how to count the number of connected components the knot diagram is…
A Lattice of Finite-Type Invariants of Virtual Knots
Micah W. Chrisman
We construct an infinite commutative lattice of groups whose dual spaces give Kauffman finite-type invariants of long virtual knots. The lattice is based "horizontally" upon the Po…
Twist Lattices and the Jones-Kauffman Polynomial for Long Virtual Knots
Micah W. Chrisman
In this paper, we investigate twist sequences for Kauffman finite-type invariants and Goussarov-Polyak-Viro finite-type invariants. It is shown that one obtains a Kauffman or GPV t…