Related papers: Positive oriented Thompson links
Let G be a connected reductive group over the complex numbers with a fixed pinning. We define and study the totally positive part of the set of maximal tori of G.
Jones introduced unitary representations of Thompson group $F$ starting from a given subfactor planar algebra, and all unoriented links arise as matrix coefficients of these representations. Moreover, all oriented links arise as matrix…
We present some partial results concerning a-T-menability of groups acting on trees. Various known results are given uniform proofs.
We introduce stable equivalence classes of oriented links in orientable three-manifolds that are orientation $I$-bundles over closed but not necessarily orientable surfaces. We call these twisted links, and show that they subsume the…
The theory of total positivity for reductive groups is here extended to the case of symmetric spaces.
We prove that Thompson's group $F$ has a generating set with two elements such that every two powers of them generate a finite index subgroup of $F$.
We reveal that Thompson's group $F$ has a quandle refinement, and we establish some essential results about the originating quandle.
We present a positivity conjecture for the coefficients of the development of Jack polynomials in terms of power sums. This extends Stanley's ex-conjecture about normalized characters of the symmetric group. We prove this conjecture for…
We will show the raitonality of some twisted symmetric group actions.
We consider random subgroups of Thompson's group $F$ with respect to two natural stratifications of the set of all $k$ generator subgroups. We find that the isomorphism classes of subgroups which occur with positive density are not the same…
Starting from the work by Jones on representations of Thompson's group $F$, subgroups of $F$ with interesting properties have been defined and studied. One of these subgroups is called the $3$-colorable subgroup $\mathcal{F}$, which…
Let S(D) be the surface produced by applying Seifert's algorithm to the oriented link diagram D. I prove that if D has no negative crossings then S(D) is a quasipositive Seifert surface, that is, S(D) embeds incompressibly on a fiber…
Structure monoids and groups are algebraic invariants of equational varieties. We show how to construct presentations of these objects from coherent categorifications of equational varieties, generalising several results of Dehornoy. We…
We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of…
We give the classification of elements - respectively cyclic subgroups - of finite order of the Cremona group, up to conjugation. Natural parametrisations of conjugacy classes, related to fixed curves of positive genus, are provided.
A large class of positive finite presentations of the braid groups is found and studied. It is shown that no presentations but known exceptions in this class have the property that equivalent braid words are also equivalent under positive…
We prove twist positivity and positivity of the pair correlation function for combined spatial and internal symmetries of free bosonic Lagrangians. We work in a general setting, extending the results obtained in Twist Positivity [1].
We characterise positive braid links with positive Seifert form via a finite number of forbidden minors. From this we deduce a one-to-one correspondence between prime positive braid links with positive Seifert form and simply laced Dynkin…
We discuss relations among various positivities of knots and links, such as strong quasipositivity and quasipositivity. We give several pieces of supporting evidence for conjectural statements concerning these positivities and the defect of…
In this note, we prove an analog of the Valiron-Titchmarsch Theorem for Positive Temperatures