Related papers: Conjugacy and Dynamics in Thompson's Groups
We develop a new framework for the study of complex continuous time dynamical systems based on viewing them as collections of interacting control modules. This framework is inspired by and builds upon the groupoid formalism of Golubitsky,…
Functional renormalisation group approach is applied to a imbalanced many- fermion system with a short-range attractive force. Composite boson field is introduced to describe the pairing between different flavour fermions. A set of…
We analyse the geometry and complexity of the conjugacy problem in a family of free-by-cyclic groups $H_m=F_m\rtimes\mathbb{Z}$ where the defining free-group automorphism is positive and polynomially growing. We prove that the conjugator…
This paper studies when a pair of elements in F are the images of the standard generators of F under a self monomorphism.
We associate to every positive braid a braid monodromy group, generalizing the geometric monodromy group of an isolated plane curve singularity. If the closure of the braid is a knot, we identify the corresponding group with a framed…
A coupled-cluster approach for systems of $N$ bosons in external traps is developed. In the coupled-cluster approach the exact many-body wavefunction is obtained by applying an exponential operator $\exp{T}$ to the ground configuration…
In our previous papers [11,13] we showed that the Hamilton-Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how…
We provide a systematic treatment of the tenfold way of classifying fermionic systems that naturally allows for the study of those with arbitrary $N$-body interactions. We identify four types of symmetries that such systems can possess,…
We prove new results about the remarkable infinite simple groups introduced by Richard Thompson in the 1960s. We define the groups as partial transformation groups and we give a faithful representation in the Cuntz C*-algebra. For the…
We extend a construction of Jones to associate $(n, n)$-tangles with elements of Thompson's group $F$ and prove that it is asymptotically faithful as $n \to\infty$. Using this construction we show that the oriented Thompson group $\vec F$…
This paper concerns the enumeration of simultaneous conjugacy classes of tuples of commuting unitary matrices and of commuting symplectic matrices over a finite field $\mathbf{F}_q$ of odd size. For any given conjugacy class, the orbits for…
Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…
Choose any oriented link type X and closed braid representatives X[+], X[-] of X, where X[-] has minimal braid index among all closed braid representatives of X. The main result of this paper is a `Markov theorem without stabilization'. It…
When animal groups move coherently in the form of a flock, their trajectories are not all parallel, the individuals exchange their position in the group. In this Letter we introduce a measure of this mixing dynamics, which we quantify as…
We show how to construct a family of groups with simple commutator subgroups from aperiodic 1-vertex, finitely aligned higher rank graphs (which are, in fact, a class of cancellative monoids). Inverse semigroups form the intermediary…
We show that Thompson's group F occurs with great frequency in the group of PL homeomorphisms of the unit interval.
We provide a general mathematical framework based on the theory of graphical models to study admixture graphs. Admixture graphs are used to describe the ancestral relationships between past and present populations, allowing for population…
Weanalyzethecomputationalcomplexityofanalgorithmtosolve the conjugacy search problem in a certain family of metabelian groups. We prove that in general the time complexity of the conjugacy search problem for these groups is at most…
The role of generalized Bowen-Franks groups (BF-groups) as topological conjugacy invariants for $\mathbb{T}^{n}$ automorphisms is studied. Using algebraic number theory, a link is established between equality of BF-groups for different…
We introduce the concept of a type system~$\Part$, that is, a partition on the set of finite words over the alphabet~$\{0,1\}$ compatible with the partial action of Thompson's group~$V$, and associate a subgroup~$\Stab{V}{\Part}$ of~$V$. We…