Virtual knots and links
By Louis H. Kauffman, V. Manturov. 2005
49 citations recorded by the source corpus.
This paper is an introduction to the subject of virtual knot theory and presents a discussion of some new specific theorems about virtual knots. The new results are as follows: Using a 3-dimensional topology approach, we prove that if a connected sum of two virtual knots K1 and K2 is trivial, then so are both K1 and K2. We establish an algorithm for recognizing virtual links that is based on the Haken-Matveev technique.
Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/46973a8518b7426b467c0aace7f95d56ef3d1c66
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In Computational Theory and Mathematics
- V. Manturov
- Vladimir Turaev
- Louis H. Kauffman
- Stefan Friedl
- Jacob Rasmussen
- Cody Armond
- Shelly L. Harvey
- Eun Soo Lee
In Discrete Mathematics and Combinatorics
- V. Manturov
- Louis H. Kauffman
- Vladimir Turaev
- Zhiyun Cheng
- Hongzhu Gao
- H. Dye
- Andrew J. Nicas
- Robin Gaudreau
In Geometry and Topology
- V. Manturov
- Louis H. Kauffman
- Vladimir Turaev
- Zhiyun Cheng
- Hongzhu Gao
- Jacob Rasmussen
- Cody Armond
- Shelly L. Harvey
Citations in the corpus
- Cobordism of knots on surfaces (2007, background): “This area has been especially active in the context of the Kauffman theory of virtual knots, see [Kau], [ KM ], [Ku].”
- Virtual knot theory-unsolved problems (2005, unknown): “See [2, 3, 4, 5, 9, 10, 11, 12, 8, 13, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 32, 34, 35, 37, 38, 39, 40, 41, 42, 44, 51, 52, 56, 59, 60, 61, 62, 63, 65, 66 , 68, 69, 71, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 85, 87, 88, 89, 84, 91, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107,”
- An Extended Bracket Polynomial for Virtual Knots and Links (2007, background): “over the ring Z[s,s−1] is an invariant of the flat virtual diagram. This module is an example of a biquandle invariant for flat virtual s. More information and definitions for biquandles can be found in [21, 22, 12]. For ou r purposes, we only need to know that the virtual graph F is non-trivial, and t”
- PARITY AND PROJECTION FROM VIRTUAL KNOTS TO CLASSICAL KNOTS (2013, background): “For exact definitions of connected sums, see [18, 10]”