UNKNOTTING VIRTUAL KNOTS WITH GAUSS DIAGRAM FORBIDDEN MOVES

By Sam Nelson. 2000

109 citations recorded by the source corpus.

The forbidden moves can be combined with Gauss diagram Reidemeister moves to obtain move sequences with which we may change any Gauss diagram (and hence any virtual knot) into any other, including in particular the unknotted diagram.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f714f5ebd61db09484af12d9f5600cfa549c9f7d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Louis H. Kauffman
2. Mario O. Bourgoin
3. Sofia Lambropoulou

In Discrete Mathematics and Combinatorics

1. Sofia Lambropoulou
2. Louis H. Kauffman
3. Mario O. Bourgoin
4. Zhiyun Cheng
5. V. Manturov
6. Hongzhu Gao
7. H. Dye

In Geometry and Topology

1. Louis H. Kauffman
2. Sofia Lambropoulou
3. Mario O. Bourgoin
4. V. Manturov
5. Zhiyun Cheng
6. Hongzhu Gao
7. Cody Armond
8. Jacob Rasmussen

Citations in the corpus

• Virtual Braids (2004, background): “It is known that any classical knot can be unknotted in the virtual category if we allow both forbidden moves [14, 23].”
• Twisted link theory (2006, background): “Note that the two obvious 3-crossing moves that involve two real crossings and one virtual crossing are forbidden because including them makes all links are equivalent to unlinks [16].”
• VIRTUAL BRAIDS AND THE L-MOVE (2005, background): “It is known that any classical knot can be unknotted in the virtual category if we allow both forbidden moves [17, 31].”