Standard
Virtual Knot Theory and Virtual Knot Cobordism. / Kauffman, Louis H.
Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016. ed. / 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. p. 67-114 (Springer Proceedings in Mathematics and Statistics; Vol. 284).
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
Harvard
Kauffman, LH 2019,
Virtual Knot Theory and Virtual Knot Cobordism. in CC Adams, CM Gordon, VFR Jones, LH Kauffman, S Lambropoulou, KC Millett, JH Przytycki, JH Przytycki, R Ricca & R Sazdanovic (eds),
Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016. Springer Proceedings in Mathematics and Statistics, vol. 284, Springer New York LLC, pp. 67-114, International Olympic Academy, 2016, Ancient Olympia, Greece,
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. In 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 (Eds.),
Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016 (pp. 67-114). (Springer Proceedings in Mathematics and Statistics; Vol. 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. In Adams CC, Gordon CM, Jones VFR, Kauffman LH, Lambropoulou S, Millett KC, Przytycki JH, Przytycki JH, Ricca R, Sazdanovic R, editors, Knots, Low-Dimensional Topology and Applications - Knots in Hellas, International Olympic Academy, 2016. Springer New York LLC. 2019. p. 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. editor / 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. pp. 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 -
