3 citations · 6 across the 10 of their papers we have counts for
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A computational study of the number of connected components of positive Thompson links
Valeriano Aiello, Stefano Iovieno
Almost a decade ago Vaughan Jones introduced a method to produce knots from elements of the Thompson groups , which was later extended to the Brown-Thompson group . In this…
An introduction to Thompson knot theory and to Jones subgroups
Valeriano Aiello
We review a constructions of knots from elements of the Thompson groups due to Vaughan Jones, which comes in two flavours: oriented and unoriented.
On the Jones polynomial modulo primes
Valeriano Aiello, Sebastian Baader, Livio Ferretti
We derive an upper bound on the density of Jones polynomials of knots modulo a prime number , within a sufficiently large degree range: . As an application, we classify k…
Arborescence of positive Thompson links
Valeriano Aiello, Sebastian Baader
We show that the links associated with positive elements of the Thompson group coincide with the closures of bipartite arborescent tangles.
Positive oriented Thompson links
Valeriano Aiello, Sebastian Baader
We prove that the links associated with positive elements of the oriented subgroup of the Thompson group are positive.
Remarks on some maximal subgroups of and on the -index of knots
Valeriano Aiello
We demonstrate that three maximal subgroups of infinite index in the rectangular subgroup \( K_{(2,2)} \) of the Thompson group \( F \), each containing Jones's \( 3 \)-colorable s…