Virtual Crossing Number and the Arrow Polynomial
By H. Dye, Louis H. Kauffman. 2008
99 citations recorded by the source corpus.
We introduce a new polynomial invariant of virtual knots and links and use this invariant to compute a lower bound on the virtual crossing number and the minimal surface genus.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a3a5bdbf4fb697a79835cb54fe6388a7fd0b5499
How researchers see this paper
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In Discrete Mathematics and Combinatorics
- Hongzhu Gao
- Zhiyun Cheng
- Louis H. Kauffman
- V. Manturov
- H. Dye
- Andrew J. Nicas
- Robin Gaudreau
- Hans U Boden
In Geometry and Topology
- Hongzhu Gao
- Zhiyun Cheng
- Louis H. Kauffman
- V. Manturov
- Cody Armond
- Jacob Rasmussen
- Shelly L. Harvey
- Eun Soo Lee
In Mathematical Physics
- Hongzhu Gao
- Zhiyun Cheng
- Louis H. Kauffman
- V. Manturov
- Cody Armond
- Jacob Rasmussen
- Shelly L. Harvey
- Eun Soo Lee
Citations in the corpus
- Parity in knot theory (2010, background): “There are many generalisations of the Kauffman bracket to virtual knots; see, for example, papers [8], [25]–[27] and the references there.”
- A polynomial invariant of virtual links (2013, methodology): “Some lower bounds of the real crossing number and virtual crossing number are obtained by studying the arrow polynomial and the Miyazawa polynomial [2, 22].”
- An Extended Bracket Polynomial for Virtual Knots and Links (2007, background): “Keywords: virtual knot theory, Jones polynomial, bracket state sum,extended bracket invariant, arrow polynomial, virtual crossing number, virtual genus Mathematics Subject Classification 2000: 57M25, 57M27”
- INTRODUCTION TO VIRTUAL KNOT THEORY (2011, methodology): “The Arrow Polynomial for Virtual and Flat Virtual Knots and Links This section describes an invariant for oriented virtual knots and links, and for flat oriented virtual knots and links that we call the arrow polynomial [4, 29].”