3 papers
math.GT2013
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…
math.GT2013
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…
math.GT2009
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…