The Extension of Knot Groups to Tangles

2005/09/28 by John Armstrong, Armstrong, John
Mathematics · #57M27 (Primary) 16B50 (Secondary) #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #math.AT #math.CT #msc:16B50 #msc:57M27

paper · pdf · doi:10.48550/arxiv.math/0509665

arxiv created 2005/09/28 · arxiv updated 2009/12/01

Abstract

The extension of the knot group π₁(S³∖ K) to the category of tangles is introduced via a new category-theoretic construction. Through this presentation, a new avenue of proof for results about knot groups is opened.

Related

• Thompson's group F, tangles, and link homology
• Conway Rational Tangles and the Thompson Group
• The groups of branched twist-spun knots
• Classification of algebraic tangles
• On the construction of knots and links from Thompson's groups