Related papers: Thompson's group T has quadratic Dehn function

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 observe that the group of all lifts of elements of Thompson's group $T$ to the real line is finitely presented and contains the additive group $\mathbb{Q}$ of the rational numbers. This gives an explicit realization of the Higman…

This Thesis presents a 2-dimensional generalization of Houghtons' groups H_n. H_n is defined to be the group of all permutations p of a disjoint union of copies of the natural numbers N, with the property that each copy of N contains a…

Let $\Gamma$ be the fundamental group of a closed, orientable, hyperbolic surface $S$. The $n$-power quotient, $\Gamma(n)$, is the quotient of $\Gamma$ by the $n$th powers of simple closed curves. We prove an analogue of the…

In this short article, we prove that any automorphism of the R. Thompson's group $F$ has infinitely many twisted conjugacy classes. The result follows from the work of Matthew Brin, together with a standard facts on R. Thompson's group $F$,…

We generalized the Lodha-Moore group into $n$-adic and showed analogues in the Lodha-Moore group of properties between the Thompson group $F$ and the generalized Thompson group $F(n)$.

We give explicit formulas for Whittaker functions for the class one principal series representations of the orthogonal groups $ SO_{2n+1}(\R) $ of odd degree. Our formulas are similar to the recursive formulas for Whittaker functions on…

We revisit our construction of the Thompson groups from the polycyclic inverse monoids in the light of new research. Specifically, we prove that the Thompson group $G_{n,1}$ is the group of units of a Boolean inverse monoid $C_{n}$ called…

We prove super-quadratic lower bounds for the growth of the filling area function of a certain class of Carnot groups. This class contains groups for which it is known that their Dehn function grows no faster than $n^2\log n$. We therefore…

The main goal of this paper is to provide a group theoretical generalization of the well-known Euler's totient function. This determines an interesting class of finite groups.

We show that the mapping class group of a handlebody of genus at least 2 has a Dehn function of at most exponential growth type.

In this paper, we prove a Liouville theorem for the $2$-Hessian equation on the Heisenberg group $\mathbb{H}^n$. The result is obtained by choosing a suitable test function and using integration by parts to derive the necessary integral…

We prove a general solvable subgroup theorem in terms of length functions. As applications, we obtain a solvable subgroup theorem in dynamical systems: any solvable group of finite Hirsch length acting on a smooth manifold with uniformly…

We prove the transformation laws of the four Jacobi theta functions using Gordon's proof for the transformation law of the Dedekind eta function.

We bound the higher-order Dehn functions and other filling invariants of certain Carnot groups using approximation techniques. These groups include the higher-dimensional Heisenberg groups, jet groups, and central products of two-step…

The authors continue a series of articles studying certain unitary representations of the Richard Thompson groups $F,T,V$ called Pythagorean. They all extend to the Cuntz algebra $\mathcal{O}$ and conversely all representations of…

We give a simple combinatorial proof that the rotation number for each element in Thompson's group ${\bf T}$ is rational.

We explicitly describe the Teichmuller space TH_n of hyperelliptic surfaces in terms of natural and effective coordinates as the space of certain (2n-6)-tuples of distinct points on the ideal boundary of the Poincare disc. We essentially…

In this paper we show that the cloning system construction of Skipper and Zaremsky [SZ21], under sufficient conditions, gives rise to Thompson-Like groups which are stable; in particular, these are McDuff groups in the sense of Deprez and…

We give a bound for the exponents of powers of Dehn twists to generate a right-angled Artin group. Precisely, if $\mathcal{F}$ is a finite collection of pairwise distinct simple closed curves on a finite type surface and if $N$ denotes the…