15 citations · 42 across the 19 of their papers we have counts for
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Prime Decomposition and Non-Commutativity in the Monoid of Long Virtual Knots
Micah W. Chrisman
It is well-known that the monoid of long virtual knots is not commutative. This contrasts with the case of classical long knots, where for all $A…
The Three Loop Isotopy and Framed Isotopy Invariants of Virtual Knots
Micah W. Chrisman, H. A. Dye
This paper introduces two virtual knot theory ``analogues'' of a well-known family of invariants for knots in thickened surfaces: the Grishanov-Vassiliev finite-type invariants of…
Fibered Knots and Virtual Knots
Micah W. Chrisman, Vassily O. Manturov
We introduce a new technique for studying classical knots with the methods of virtual knot theory. Let be a knot and a knot in the complement of with …
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…