INTRODUCTION TO VIRTUAL KNOT THEORY

By Louis H. Kauffman. 2011

97 citations recorded by the source corpus.

This paper is an introduction to virtual knot theory and an exposition of new ideas and constructions, including the parity bracket polynomial, the arrow polynomial, the parity arrow polynomial and categorifications of the arrow polynomial.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/77bd611fd660d72a1d5fa3e57061b67678999508

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In Discrete Mathematics and Combinatorics

1. Hongzhu Gao
2. Zhiyun Cheng
3. Louis H. Kauffman
4. V. Manturov
5. H. Dye

In Geometry and Topology

1. Hongzhu Gao
2. Zhiyun Cheng
3. Louis H. Kauffman
4. V. Manturov
5. Cody Armond
6. Jacob Rasmussen
7. Shelly L. Harvey
8. Eun Soo Lee

In Mathematical Physics

1. Hongzhu Gao
2. Zhiyun Cheng
3. Louis H. Kauffman
4. Cody Armond
5. V. Manturov
6. Jacob Rasmussen
7. Shelly L. Harvey
8. Eun Soo Lee

Citations in the corpus

• A polynomial invariant of virtual knots (2012, background): “Finally we discuss which kind of polynomial can be realized as fK(t) for some virtual knot K. Keywords virtual knot; odd writhe polynomial MR(2000) Subject Classification 57M25”
• A polynomial invariant of virtual links (2013, methodology): “We remark that the definition with this viewpoint can be regarded as an application of the Long Flat Embedding Theorem in [13].”
• An Affine Index Polynomial Invariant of Virtual Knots (2012, methodology): “For more information the reader is referred to [17, 10, 19, 20, 21, 24].”