@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",
}