Thompson's group F, tangles, and link homology

2024/03/25 by Krushkal, Vyacheslav, Liles, Louisa, Luo, Yangxiao
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2403.16838

Abstract

We extend a construction of Jones to associate (n, n)-tangles with elements of Thompson's group F and prove that it is asymptotically faithful as n →∞. Using this construction we show that the oriented Thompson group F admits a lax group action on a category of Khovanov's chain complexes.

Related

• On the construction of knots and links from Thompson's groups
• Conway Rational Tangles and the Thompson Group
• The number of connected components of links associated with the Thompson group
• On Thompson knot theory and conjugacy classes of Thompson's group F
• Classification of Thompson related groups arising from Jones technology I