Related papers: Positive oriented Thompson links

We prove that commutator subgroups of topological full groups arising from minimal subshifts have exponential growth. We also prove that the measurable full group associated to the countable, measure-preserving, ergodic and hyperfinite…

We study the positive theory of groups acting on trees and show that under the presence of weak small cancellation elements, the positive theory of the group is trivial, i.e. coincides with the positive theory of a non-abelian free group.…

We show that any proper Lie groupoid admits a compatible (real) analytic structure.

The authors classify the finite index subgroups of R. Thompson's group $F$. All such groups that are not isomorphic to $F$ are non-split extensions of finite cyclic groups by $F$. The classification describes precisely which finite index…

In this paper, we prove that the (orientation-preserving) symmetry groups of $b$-prime flat fully augmented links correspond exactly with the finite subgroups of $O(3)$. We accomplish this by first developing a dictionary between…

We propose new conjectures about the relationship between the principal blocks of finite groups for different primes and establish evidence for these conjectures.

We show that Thompson's group F is the symmetry group of the "generic idempotent". That is, take the monoidal category freely generated by an object A and an isomorphism A \otimes A --> A; then F is the group of automorphisms of A.

In this paper we prove that the general version, F(N) of the Thompson group is inner amenable. As a consequence we generalize a result of P.Jolissaint. To do so, we prove first that F(N) together with a normal subgroup are i.c.c (infinite…

We prove an explicit formula for the tail of the colored Jones polynomial for a class of arborescent links in terms of a product of theta functions and/or false theta functions. We also provide numerical evidence towards a classification of…

It is shown that the restriction of the action of any group with finite orbit on the minimal sets of dendrites is equicontinuous. Consequently, we obtain that the action of any amenable group and Thompson group on dendrite restricted on…

We construct approximately inner actions of discrete amenable groups on strongly amenable subfactors of type II_1 with given invariants, and obtain classification results under some conditions. We also study the lifting of the relative \chi…

We show that one can naturally describe elements of R. Thompson's finitely presented infinite simple group $V$, known by Thompson to have a presentation with four generators and fourteen relations, as products of permutations analogous to…

We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…

Given certain intersection cohomology sheaves on a projective variety with a torus action, we relate the cohomology groups of their tensor product to the cohomology groups of the individual sheaves. We also prove a similar result in the…

We link the study of positive quantum maps, block positive operators, and entanglement witnesses with problems related to multivariate polynomials. For instance, we show how indecomposable block positive operators relate to biquadratic…

It is shown that finitely presented icc inner amenable groups yield strongly 1-bounded II_1 factors.

We show that Thompson's $A\times B$-Lemma can be obtained as a consequence of the Brauer pair version of Brauer's Third Main Theorem.

A general result of Epstein and Thurston implies that all link groups are automatic, but the proof provides no explicit automaton. Here we show that the groups of all torus links are groups of fractions of so-called Garside monoids, i.e.,…

We investigate positive-dimensional closed reductive subgroups of almost simple algebraic groups containing a regular unipotent element. Our main result states that such subgroups do not lie inside proper parabolic subgroups unless possibly…

We show that the adjoint group of the Alexander quandle associated to an abelian group M and an automorphism T has a nice description in terms of M and T.