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Virtual knot cobordism and the affine index polynomial

Louis H. Kauffman

Department of Mathematics, Statistics and Computer Science, 851 South Morgan Street, University of Illinois at Chicago, Chicago, Illinois 60607-7045, USA

Department of Mechanics and Mathematics, Novosibirsk State University, Novosibirsk, Russia

E-mail Address: kauffman@uic.edu

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https://doi.org/10.1142/S0218216518430174Cited by:7 (Source: Crossref)

This article is part of the issue:

Special Issue — Self-Distributive System and Quandle (Co)Homology Theory in Algebra and Low-Dimensional Topology; Guest Editors: Y. Bae, S. Kamada, A. Kawauchi and S. Y. Lee

Abstract

This paper studies cobordism and concordance for virtual knots. We define the affine index polynomial, prove that it is a concordance invariant for knots and links (explaining when it is defined for links), show that it is also invariant under certain forms of labeled cobordism and study a number of examples in relation to these phenomena. Information on determinations of the four-ball genus of some virtual knots is obtained by via the affine index polynomial in conjunction with results on the genus of positive virtual knots using joint work with Dye and Kaestner.

Keywords:

AMSC: 57M25, 57M27

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