ALEXANDER GROUPS AND VIRTUAL LINKS

By Daniel S. Silver, Susan G. Williams. 2001

80 citations recorded by the source corpus.

Subfields: Computer Graphics and Computer-Aided Design, Control and Systems Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6b9f6b8026fe6dbbc90c8862250ab3761e99e664

How researchers see this paper

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

In Computer Graphics and Computer-Aided Design

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

In Control and Systems Engineering

1. Louis H. Kauffman
2. D. Radford
3. V. Manturov

In Geometry and Topology

1. Louis H. Kauffman
2. V. Manturov
3. J. Scott Carter
4. Mohamed Elhamdadi
5. Andrew J. Nicas
6. Robin Gaudreau
7. Hans U Boden
8. Lindsay White

Citations in the corpus

• Virtual knot groups and almost classical knots (2015, methodology): “In [3], we proved a formula relating the virtual Alexander polynomial HK(s, t, q) to the generalized Alexander polynomial GK(s, t) defined by Sawollek [30], and in equivalent forms by Kauffman–Radford [19], Manturov [23], and Silver–Williams [31, 32].”
• Virtual knots and links (2005, background): “To date, many invariants of classical knots have been generalized for the virtual case, see [GPV, KaV, KR, Ma1, Ma2, Ma8, Ma10, Saw, SW ].”
• Knot Diagrammatics (2004, methodology): “This is related to observations by Silver and Williams [139], Manturov [112, 113] and by Satoh [135] showing that the fundamental group of a virtual knot can be interpreted as the fundamental group of the complement of a torus embedded in four-dimensional Euclidean space.”
• Bi-oriented Quantum Algebras, and a Generalized Alexander Polynomial for Virtual Links (2001, methodology): “Silver and Williams first define a group.”
• Homology theory for the set-theoretic Yang–Baxter equation and knot invariants from generalizations of quandles (2002, background): “The fundamental (Wirtinger) groups of virtual knots were studied [22, 28] and their geometric interpretations were given [17].”
• Virtual knot theory-unsolved problems (2005, unknown): “…[23] [24] [25] [26] [31] [33] [34] [36] [37] [38] [39] [40] [41] [43] [50] [51] [55] [58] [59] [60] [61] [62] [64] [65] [67] [68] [70] [72] [73] [74] [75] [76] [78] [79] [80] [81] [82] [84] [86] [87] [88] [83] [90] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102] [103] [104] [105] [106] [109].”