Related papers: Positive oriented Thompson links
We discuss when homogeneous quasipositive links are positive. In particular, we show that a homogeneous diagram of a quasipositive link whose number of Seifert circles is equal to the braid index is a positive diagram.
We present sufficient conditions for total positivity of Riordan arrays. As applications we show that many well-known combinatorial triangles are totally positive and many famous combinatorial numbers are log-convex in a unified approach.
In this paper it is proved that the pure braided Thompson's group BF admits a bi-order, analog to the bi-order of the pure braid groups.
We present a simple functional integration based proof that the semigroups generated by the ultraviolet-renormalized translation-invariant non- and semi-relativistic Nelson Hamiltonians are positivity improving (and hence ergodic) with…
A remarkable result of Thompson states that a finite group is soluble if and only if its two-generated subgroups are soluble. This result has been generalized in numerous ways, and it is in the core of a wide area of research in the theory…
We prove a connectedness result for products of weighted projective spaces.
We prove that Thompson's groups $F$ and $V$ are the geometry groups of associativity, and of associativity together with commutativity, respectively. We deduce new presentations of $F$ and $V$. These presentations lead to considering a…
We construct the complete invariant for fused links. It is proved that the set of equivalence classes of $n$-component fused links is in one-to-one correspondence with the set of elements of the abelization $UVP_n/UVP_n^{\prime}$ up to…
For a positive braid link, a link represented as a closed positive braids, we determine the first few coefficients of its HOMFLY polynomial in terms of geometric invariants such as, the maximum euler characteristics, the number of split…
We generalize an algorithm of Rudolph to establish that every link is topologically concordant to a strongly quasipositive link.
We study the homology of pointed sets over a partially commutative monoid.
We prove that the braided Thompson's groups $V_{\rm br}$ and $F_{\rm br}$ are of type $F_\infty$, confirming a conjecture by John Meier. The proof involves showing that matching complexes of arcs on surfaces are highly connected. In an…
We propose a new unifying framework for Thompson-like groups using a well-known device called operads and category theory as language. We discuss examples of operad groups which have appeared in the literature before. As a first…
In this paper, we show that a link which has a positive and almost alternating diagram is alternating, besides that a positive and non-alternating Montesinos link has an almost positive-alternating diagram.
We give a short, geometric proof of Graham's theorem on positivity in the equivariant cohomology of a flag variety, based on a transversality argument.
We prove a positivity result for the T-equivariant K-theory of flag varieties associated to any symmetrizable Kac-Moody group.
Closed subgroups of the group of isometries of the regular tree $\treeq$ that fix an end of the tree and are vertex-transitive are shown to correspond, on one hand, to self-replicating groups acting on rooted trees and, on the other hand,…
We compute the triply graded Khovanov-Rozansky homology of a family of links, including positive torus links and $\operatorname{Sym}^l$-colored torus knots.
We prove that Thompson's group $T$ and, more generally, all the Higman-Thompson groups $T_n$ have quadratic Dehn function.
In this article we revisit a new notion of positivity in real semisimple Lie groups that at the same time generalizes total positivity in split real Lie groups as well as positive Lie semigroups in Hermitian Lie groups of tube type. We…