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Virtual Knot Theory and Virtual Knot Cobordism. / Kauffman, Louis H.
Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016. ред. / Colin C. Adams; Cameron McA. Gordon; Vaughan F.R. Jones; Louis H. Kauffman; Sofia Lambropoulou; Kenneth C. Millett; Jozef H. Przytycki; Jozef H. Przytycki; Renzo Ricca; Radmila Sazdanovic. Springer New York LLC, 2019. стр. 67-114 (Springer Proceedings in Mathematics and Statistics; Том 284).
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Harvard
Kauffman, LH 2019,
Virtual Knot Theory and Virtual Knot Cobordism. в CC Adams, CM Gordon, VFR Jones, LH Kauffman, S Lambropoulou, KC Millett, JH Przytycki, JH Przytycki, R Ricca & R Sazdanovic (ред.),
Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016. Springer Proceedings in Mathematics and Statistics, Том. 284, Springer New York LLC, стр. 67-114, International Olympic Academy, 2016, Ancient Olympia, Греция,
17.07.2016.
https://doi.org/10.1007/978-3-030-16031-9_4APA
Kauffman, L. H. (2019).
Virtual Knot Theory and Virtual Knot Cobordism. в C. C. Adams, C. M. Gordon, V. F. R. Jones, L. H. Kauffman, S. Lambropoulou, K. C. Millett, J. H. Przytycki, J. H. Przytycki, R. Ricca, & R. Sazdanovic (Ред.),
Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016 (стр. 67-114). (Springer Proceedings in Mathematics and Statistics; Том 284). Springer New York LLC.
https://doi.org/10.1007/978-3-030-16031-9_4Vancouver
Kauffman LH.
Virtual Knot Theory and Virtual Knot Cobordism. в Adams CC, Gordon CM, Jones VFR, Kauffman LH, Lambropoulou S, Millett KC, Przytycki JH, Przytycki JH, Ricca R, Sazdanovic R, Редакторы, Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016. Springer New York LLC. 2019. стр. 67-114. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-030-16031-9_4
Author
Kauffman, Louis H. /
Virtual Knot Theory and Virtual Knot Cobordism. Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016. Редактор / Colin C. Adams ; Cameron McA. Gordon ; Vaughan F.R. Jones ; Louis H. Kauffman ; Sofia Lambropoulou ; Kenneth C. Millett ; Jozef H. Przytycki ; Jozef H. Przytycki ; Renzo Ricca ; Radmila Sazdanovic. Springer New York LLC, 2019. стр. 67-114 (Springer Proceedings in Mathematics and Statistics).
BibTeX
@inproceedings{abb7e5bddd5545408a70e9de7630bac3,
title = "Virtual Knot Theory and Virtual Knot Cobordism",
abstract = "This paper is an introduction to virtual knot theory and virtual knot cobordism [37, 39]. Non-trivial examples of virtual slice knots are given and determinations of the four-ball genus of positive virtual knots are explained in relation to joint work with Dye and Kaestner [12]. We study the affine index polynomial [38], prove that it is a concordance invariant, show that it is invariant also under certain forms of labeled cobordism and study a number of examples in relation to these phenomena. In particular we show how a mod-2 version of the affine index polynomial is a concordance invariant of flat virtual knots and links, and explore a number of examples in this domain.",
keywords = "Affine index polynomial, Arrow polynomial, Bracket polynomial, Cobordism, Concordance, Graph, Invariant, Knot, Link, Parity bracket polynomial, Virtual knot",
author = "Kauffman, {Louis H.}",
note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2019.; International Olympic Academy, 2016 ; Conference date: 17-07-2016 Through 23-07-2016",
year = "2019",
month = jan,
day = "1",
doi = "10.1007/978-3-030-16031-9_4",
language = "English",
isbn = "9783030160302",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer New York LLC",
pages = "67--114",
editor = "Adams, {Colin C.} and Gordon, {Cameron McA.} and Jones, {Vaughan F.R.} and Kauffman, {Louis H.} and Sofia Lambropoulou and Millett, {Kenneth C.} and Przytycki, {Jozef H.} and Przytycki, {Jozef H.} and Renzo Ricca and Radmila Sazdanovic",
booktitle = "Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016",
address = "United States",
}
RIS
TY - GEN
T1 - Virtual Knot Theory and Virtual Knot Cobordism
AU - Kauffman, Louis H.
N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2019.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - This paper is an introduction to virtual knot theory and virtual knot cobordism [37, 39]. Non-trivial examples of virtual slice knots are given and determinations of the four-ball genus of positive virtual knots are explained in relation to joint work with Dye and Kaestner [12]. We study the affine index polynomial [38], prove that it is a concordance invariant, show that it is invariant also under certain forms of labeled cobordism and study a number of examples in relation to these phenomena. In particular we show how a mod-2 version of the affine index polynomial is a concordance invariant of flat virtual knots and links, and explore a number of examples in this domain.
AB - This paper is an introduction to virtual knot theory and virtual knot cobordism [37, 39]. Non-trivial examples of virtual slice knots are given and determinations of the four-ball genus of positive virtual knots are explained in relation to joint work with Dye and Kaestner [12]. We study the affine index polynomial [38], prove that it is a concordance invariant, show that it is invariant also under certain forms of labeled cobordism and study a number of examples in relation to these phenomena. In particular we show how a mod-2 version of the affine index polynomial is a concordance invariant of flat virtual knots and links, and explore a number of examples in this domain.
KW - Affine index polynomial
KW - Arrow polynomial
KW - Bracket polynomial
KW - Cobordism
KW - Concordance
KW - Graph
KW - Invariant
KW - Knot
KW - Link
KW - Parity bracket polynomial
KW - Virtual knot
UR - http://www.scopus.com/inward/record.url?scp=85069176625&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-16031-9_4
DO - 10.1007/978-3-030-16031-9_4
M3 - Conference contribution
AN - SCOPUS:85069176625
SN - 9783030160302
T3 - Springer Proceedings in Mathematics and Statistics
SP - 67
EP - 114
BT - Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016
A2 - Adams, Colin C.
A2 - Gordon, Cameron McA.
A2 - Jones, Vaughan F.R.
A2 - Kauffman, Louis H.
A2 - Lambropoulou, Sofia
A2 - Millett, Kenneth C.
A2 - Przytycki, Jozef H.
A2 - Przytycki, Jozef H.
A2 - Ricca, Renzo
A2 - Sazdanovic, Radmila
PB - Springer New York LLC
T2 - International Olympic Academy, 2016
Y2 - 17 July 2016 through 23 July 2016
ER -
