相关论文: Thompson's Group F is not Minimally Almost Convex

Let $F(p)$, $p\ge2$ be the family of generalized Thompson's groups. Here F(2) is the famous Richard Thompson's group usually denoted by $F$. We find the growth rate of the monoid of positive words in $F(p)$ and show that it does not exceed…

We study subgroups of Thompson's group $F$ by means of an automaton associated with them. We prove that every maximal subgroup of $F$ of infinite index is closed, that is, it coincides with the subgroup of $F$ accepted by the automaton…

The Shapley-Folkman theorem shows that Minkowski averages of uniformly bounded sets tend to be convex when the number of terms in the sum becomes much larger than the ambient dimension. In optimization, Aubin and Ekeland [1976] show that…

The purpose of this note is to prove a lower bound on the Folner function for Thompson's groups F.

Based on the convergence of their infinitesimal generators in the mixed topology, we provide a stability result for strongly continuous convex monotone semigroups on spaces of continuous functions. In contrast to previous results, we do not…

This article is dedicated to the study of asymptotically rigid mapping class groups of infinitely-punctured surfaces obtained by thickening planar trees. Such groups include the braided Ptolemy-Thompson groups $T^\sharp,T^\ast$ introduced…

We prove an acylindrical accessibility theorem for finitely generated groups acting on $\mathbf R$-trees. Namely, we show that if $G$ is a freely indecomposable non-cyclic $k$-generated group acting minimally and $M$-acylindrically on an…

We prove that seesaw words exist in Thompson's Group F(N) for N=2,3,4,... with respect to the standard finite generating set X. A seesaw word w with swing k has only geodesic representatives ending in g^k or g^{-k} (for given g\in X) and at…

A subset $S$ of a group $G$ invariably generates $G$ if $G= \langle s^{g(s)} | s \in S\rangle$ for every choice of $g(s) \in G,s \in S$. We say that a group $G$ is invariably generated if such $S$ exists, or equivalently if $S=G$ invariably…

In the aftermath of the Robertson--Seymour Graph Minor Theorem, Thomas conjectured that the countable graphs are well-quasi-ordered under the minor relation. We prove that this conjecture, when restricted to graphs with no infinite paths…

There is a map, defined and studied by Jones, from Thompson's group $F$ to knots. Jones proved that every knot is in the image of this map -- that is, that every knot can be seen as the "knot closure" of a Thompson group element. We…

We show that several classes of groups G of PL-homeomorphisms of the real line admit non-trivial homomorphisms from G to the additive group of reals that are fixed by every automorphism of G. The classes of groups enjoying the stated…

Vaughan Jones discovered unexpected connections between Richard Thompson's group and subfactor theory while attempting to construct conformal field theories (in short CFT). Among other this founded Jones' technology: a powerful new method…

A topological group is minimal if it does not admit a strictly coarser Hausdorff group topology. We provide a sufficient and necessary condition for the minimality of the semidirect product $G\leftthreetimes P,$ where $G$ is a compact…

In the spirit of peripheral subgroups in relatively hyperbolic groups, we exhibit a simple class of quasi-isometrically rigid subgroups in graph products of finite groups, which we call eccentric subgroups. As an application, we prove that,…

Let $G$ be an abelian group. We prove that a group $G$ admits a Hausdorff group topology $\tau$ such that the von Neumann radical $\mathbf{n}(G, \tau)$ of $(G, \tau)$ is non-trivial and finite iff $G$ has a non-trivial finite subgroup. If…

We construct an explicit infinite family of pairwise non-isomorphic infinite simple groups of type $\mathrm{F}_\infty$ (in particular, they are finitely presented) that act faithfully on the circle by orientation-preserving homeomorphisms,…

We consider diagram groups as defined by V. Guba and M. Sapir. A diagram group G acts on the associated cube complex K by isometries. It is known that if a cube complex L is of a finite dimension then every isometry g of L is semi-simple,…

We prove that the lower central series of the cactus group associated with a non commutative Coxeter group never stabilizes. We also compute a minimal presentation in terms of generators for the cactus group associated with a finite Coxeter…

Consider an equidimensional faithful conical action of an algebraic torus $T$ on an affine normal conical variety $X$ over an algebraically closed field of characteristic zero. Then there exists a finite normal subgroup $N$ of $T$ such that…