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4 papers · 1 filter
Virtual Knot Diagrams and the Witten-Reshetikhin-Turaev Invariant
H. A. Dye, Louis H. Kauffman
The Witten-Reshetikhin-Turaev invariant of classical link diagrams is generalized to virtual link diagrams. This invariant is unchanged by the framed Reidemeister moves and the Kir…
Sub-Finsler geometry in dimension three
Jeanne N. Clelland, Christopher G. Moseley
We define the notion of sub-Finsler geometry as a natural generalization of sub-Riemannian geometry with applications to optimal control theory. We compute a complete set of local…
Virtual knots undetected by 1 and 2-strand bracket polynomials
H. A. Dye
Kishino's knot is not detected by the fundamental group or the bracket polynomial; these invariants cannot differentiate between Kishino's knot and the unknot. However, we can show…
Minimal surface representations of virtual knots and links
H. A. Dye, Louis H. Kauffman
Kuperberg [Algebr. Geom. Topol. 3 (2003) 587-591] has shown that a virtual knot corresponds (up to generalized Reidemeister moves) to a unique embedding in a thichened surface of m…