51 citations
- Tongji UniversityCN2 papers
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4 papers · 1 filter
Virtual knot cobordism and bounding the slice genus
Hans U. Boden, Micah Chrisman, Robin Gaudreau
In this paper, we compute the slice genus for many low-crossing virtual knots. For instance, we show that 1295 out of 92800 virtual knots with 6 or fewer crossings are slice, and t…
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…
On the Goussarov-Polyak-Viro Finite-Type Invariants and the Virtualization Move
Micah W. Chrisman
In this paper, it is shown that there are no nonconstant Goussarov-Polyak-Viro finite-type invariants that are invariant under the virtualization move. As an immediate corollary, w…
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…