TY - JOUR

T1 - Virtual knot cobordism and the affine index polynomial

AU - Kauffman, Louis H.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - 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.

AB - 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.

KW - affine index polynomial

KW - cobordism

KW - concordance

KW - invariant

KW - Khovanov homology

KW - Knot

KW - knotoid

KW - labeled cobordism

KW - link

KW - Rasmussen invariant

KW - virtual knot

KW - INVARIANT

UR - http://www.scopus.com/inward/record.url?scp=85052931273&partnerID=8YFLogxK

U2 - 10.1142/S0218216518430174

DO - 10.1142/S0218216518430174

M3 - Article

AN - SCOPUS:85052931273

VL - 27

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 11

M1 - 1843017

ER -