Related papers: An Irrational-slope Thompson's Group

The word problem for Thompson's group $F$ has a solution, but it remains unknown whether $F$ is automatic or has a finite or regular convergent (terminating and confluent) rewriting system. We show that the group $F$ admits a natural…

Recently, Jones introduced a method of constructing knots and links from elements of Thompson's group $F$ by using its unitary representations. He also defined several subgroups of $F$ as the stabilizer subgroups and some researchers…

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…

We introduce a combinatorial characterization of simpliciality for arrangements of hyperplanes. We then give a sharp upper bound for the number of hyperplanes of such an arrangement in the projective plane over a finite field, and present…

We study an abstract group of reversible Turing machines. In our model, each machine is interpreted as a homeomorphism over a space which represents a tape filled with symbols and a head carrying a state. These homeomorphisms can only…

In a "naive" attempt to create algebraic quantum field theories on the circle, we obtain a family of unitary representations of Thompson's groups T and F for any subfactor. The Thompson group elements are the "local scale transformations"…

In this paper, we solve the conjugacy problem for Topological Full Groups of Irreducible Edge Shifts, introduced by Matui in 2015 and later recontextualized as groups of almost automorphisms of trees by Lederle in 2020. The techniques we…

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…

We introduce the concept of a generic Euclidean triangle $\tau$ and study the group $G_\tau$ generated by the reflection across the edges of $\tau$. In particular, we prove that the subgroup $T_\tau$ of all translations in $G_\tau$ is free…

This paper introduces iterated monodromy groups for transcendental functions and discusses them in the simplest setting, for post-singularly finite exponential functions. These groups are self-similar groups in a natural way, based on an…

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…

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…

Jones introduced unitary representations for the Thompson groups $F$ and $T$ from a given subfactor planar algebra. Some interesting subgroups arise as the stabilizer of certain vector, in particular the Jones subgroups $\vec{F}$ and…

We endow a topological group $(G, \tau)$ with a coarse structure defined by the smallest group ideal $S_{\tau} $ on $G$ containing all converging sequences with their limits and denote the obtained coarse group by $(G, S_{\tau})$. If $G$ is…

We introduce a linearly ordered lattice $\mu(Grp)$ of torsion theories in simplicial groups. The torsion theories are defined where the torsion/torsion-free subcategories are given by the simplicial groups with bounded above/below Moore…

We show that double cosets of the infinite symmetric group with respect to some special subgroups admit natural structures of semigroups. We interpret elements of such semigroups in combinatorial terms (chips, colored graphs,…

Symmetry of geometrical figures is reflected in regularities of their algebraic invariants. Algebraic regularities are often preserved when the geometrical figure is topologically deformed. The most natural, intuitively simple but…

Various descending chains of subgroups of a finite permutation group can be used to define a sequence of `basic' permutation groups that are analogues of composition factors for abstract finite groups. Primitive groups have been the…

Using F-theory we construct 4D ${\cal N}=1$ SUGRA theories with the Standard Model gauge group, three chiral generations, and matter parity in order to forbid all dimension four baryon and lepton number violating operators. The underlying…

Thompson's theorem stated that a finite group $G$ is solvable if and only if every $2$-generated subgroup of $G$ is solvable. In this paper, we prove some new criteria for both solvability and nilpotency of a finite group using certain…