Tied links in the solid torus

2019/10/23 by Flores, Marcelo
#05A18 #20C08 #20F36 #20F55 #57M25 #57M27 #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1910.10778

Abstract

We introduce the concept of tied links in the solid torus, which generalize naturally the concept of tied links in S³ previously introduced by Aicardi and Juyumaya. We also define an invariant of these tied links by using skein relations, and subsequently we recover this invariant by using Jones' method over the bt-algebra of type \mathttB and the Markov trace defined on this.

Related

• A bt-algebra of type B
• Classification of small links in the unmarked solid torus
• Tied Links in various topological settings
• A 1-parameter approach to links in a solid torus
• On Rational Knots and Links in the Solid Torus