The number of connected components of links associated with the Thompson group

2019/10/11 by Aiello, Valeriano
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1910.05045

Abstract

A few years ago Vaughan Jones devised a method to construct knots and links from elements of the Thompson groups. Given an element g of F₃ we construct a permutation P(g) which we call its Thompson permutation. By analogy with the braid group, we show that the number of the connected components of the link L(g) is equal to the number of orbits of its Thompson permutation.

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