1,721,092 research outputs found
An introduction to Thompson knot theory and to Jones subgroups
Full text linkWe review a constructions of knots from elements of the Thompson groups due to Vaughan Jones, which comes in two flavors: oriented and unoriented
On the Alexander theorem for the oriented Thompson group \overarrow F
No full textIn [10] and [12] Vaughan Jones introduced a construction which yields oriented knots and links from elements of the oriented Thompson group F. In this paper we prove, by analogy with Alexander’s classical theorem establishing that every knot or link can be represented as a closed braid, that given an oriented knot /link L, there exists an element g in F whose closure L(g) is L
ON THE 3-COLORABLE SUBGROUP F and MAXIMAL SUBGROUPS OF THOMPSON’S GROUP F
Full text linkIn his work on representations of Thompson’s group F, Vaughan Jones defined and studied the 3-colorable subgroup F of F. Later, Ren showed that it is isomorphic to the Brown–Thompson group F4. In this paper we continue with the study of the 3-colorable subgroup and prove that the quasi-regular representation of F associated with the 3-colorable subgroup is irreducible. We show in addition that the preimage of F under a certain injective endomorphism of F is contained in three (explicit) maximal subgroups of F of infinite index. These subgroups are different from the previously known infinite index maximal subgroups of F, namely the parabolic subgroups that fix a point in (0, 1), (up to isomorphism) the Jones’ oriented subgroup F⃗ , and the explicit examples found by Golan
On the cyclic automorphism of the Cuntz algebra and its fixed-point algebra
Full text linkWe investigate the structure of the fixed-point algebra of On under the action of the cyclic permutation of the generating isometries. We prove that it is ⁎-isomorphic with On, thus generalizing a result of Choi and Latrémolière on O2. As an application of the technique employed, we also describe the fixed-point algebra of O2n under the exchange automorphism
ARBORESCENCE OF POSITIVE THOMPSON LINKS
Full text linkWe show that the links associated with positive elements of the Thompson group F coincide with the closures of bipartite arborescent tangles
On the oriented Thompson subgroup F → 3 and its relatives in higher Brown-Thompson groups
Full text linkA few years ago the so-called oriented subgroup F→ of the Thompson group F was introduced by V. Jones while investigating the connections between subfactors and conformal field theories. In the coding of links and knots by elements of F it corresponds exactly to the oriented ones. Thanks to the work of Golan and Sapir, F→ provided the first example of a maximal subgroup of infinite index in F different from the parabolic subgroups that fix a point in (0, 1). In this paper we investigate possible analogues of F→ in higher Thompson groups Fk,k ≥ 2, with F = F2, introduced by Brown. Most notably, we study algebraic properties of the oriented subgroup F→3 of F3, as described recently by Jones, and prove in particular that it gives rise to a non-parabolic maximal subgroup of infinite index in F3 and that the corresponding quasi-regular representation is irreducible
The Jones polynomial and functions of positive type on the oriented Jones–Thompson groups F→ and T→
No full textThe pioneering work of Jones and Kauffman unveiled a fruitful relationship between statistical mechanics and knot theory. Recently, Jones introduced two subgroups F→ and T→ of the Thompson groups F and T, respectively, together with a procedure that associates an oriented link diagram to any element of these subgroups. Moreover, several specializations of some well-known polynomial link invariants can be seen as functions of positive type on the Thompson groups or the Jones–Thompson subgroups. One important example is provided by suitable evaluations of the Jones polynomial, which are thus associated with certain unitary representations of the groups F→ and T→. Within this framework, we discuss an alternative approach that relies on some partition function interpretation of the Jones polynomial, and also exhibit more examples associated with other link invariants, notably the two-variable Kauffman polynomial and the HOMFLY polynomial. In the unoriented case, extending our previous results, we also show by similar methods that certain evaluations of the Tutte polynomial and of the Kauffman bracket, suitably renormalized, yield functions of positive type on T
Vibrazioni prodotte da infrastrutture di trasporto: una proposta metodologica per previsioni quantitative.
No full textVibrazioni prodotte da infrastrutture di trasporto in ambiente urbano: una proposta metodologica applicata ad un caso di studio.
No full textVibrazioni prodotte da infrastrutture di trasporto: una proposta metodologica per previsioni quantitative.
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