TY - JOUR

T1 - Concordance of certain 3-braids and Gauss diagrams

AU - Brandenbursky, Michael

N1 - Funding Information:
This work was initiated during author's stay in CRM-ISM Montreal. The author was partially supported by the CRM-ISM fellowship. He would like to thank CRM-ISM Montreal for the support and great research atmosphere.
Publisher Copyright:
© 2016 Elsevier B.V.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - Let β:=σ1σ2−1 be a braid in B3, where B3 is the braid group on 3 strings and σ1, σ2 are the standard Artin generators. We use Gauss diagram formulas to show that for each natural number n not divisible by 3 the knot which is represented by the closure of the braid βn is algebraically slice if and only if n is odd. As a consequence, we deduce some properties of Lucas numbers.

AB - Let β:=σ1σ2−1 be a braid in B3, where B3 is the braid group on 3 strings and σ1, σ2 are the standard Artin generators. We use Gauss diagram formulas to show that for each natural number n not divisible by 3 the knot which is represented by the closure of the braid βn is algebraically slice if and only if n is odd. As a consequence, we deduce some properties of Lucas numbers.

KW - Braids

KW - Concordance

KW - Gauss diagrams

KW - Knots

UR - http://www.scopus.com/inward/record.url?scp=84994201972&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2016.10.006

DO - 10.1016/j.topol.2016.10.006

M3 - Article

AN - SCOPUS:84994201972

SN - 0166-8641

VL - 214

SP - 180

EP - 185

JO - Topology and its Applications

JF - Topology and its Applications

ER -