Related papers: Bowen-Franks groups as conjugacy invariants for $\…
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…
In this article we generalize a theorem of Benson for generalized quadrangles to strongly regular graphs and directed strongly regular graphs. The main result provides numerical restrictions on the number of fixed vertices and the number of…
Every indefinite binary form occurs as the Picard lattice of some K3-surface. The group of its isometries, or automorphs, coincides with the automorphism group of the K3-surface, but only up to finite groups. The classical theory of…
We present sufficient conditions for the triviality of the automorphism group of regular Toeplitz subshifts and give a broad class of examples from the class of $\mathcal{B}$-free subshifts satisfying them, extending [10]. On the other hand…
2-Chern-Simons theory, or more commonly known as 4d BF-BB theory with gauged shift symmetry, is a natural generalization of Chern-Simons theory to 4-dimensional manifolds. It is part of the bestiary of higher-homotopy Maurer-Cartan…
Given two automorphisms of a group $G$, one is interested in knowing whether they are conjugate in the automorphism group of $G$, or in the abstract commensurator of $G$, and how these two properties may differ. When $G$ is the fundamental…
In this article we show how to calculate the group of automorphisms of flat K\"ahler manifolds. Moreover we are interested in the problem of classification of such manifolds up to biholomorphism. We consider these problems from two points…
The lattice of subgroups of a group is the subject of numerous results revolving around the central theme of decomposing the group into "chunks" (subquotients) that can then be compared to one another in various ways. Examples of results in…
Homogeneous Boltzmann-type equations are an established tool for modelling interacting multi-agent systems in sociophysics by means of the principles of statistical mechanics and kinetic theory. A customary implicit assumption is that…
We study the structure of generalized Baumslag-Solitar groups from the point of view of their (usually non-unique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of…
For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group,…
The main object of study of the present paper is the group $\au_n$ of \emph{unimodular automorphisms} of $\com^n$. Taking $\au_n$ as a working example, our intention was to develop an approach (or rather an edifice) which allows one to…
We construct a generalization of pure lattice gauge theory (LGT) where the role of the gauge group is played by a tensor category. The type of tensor category admissible (spherical, ribbon, symmetric) depends on the dimension of the…
Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological…
This work is a continuation of Automorphisms of $K$-groups I, P. Flavell, preprint. The main object of study is a finite $K$-group $G$ that admits an elementary abelian group $A$ acting coprimely. For certain group theoretic properties…
Topological order in two-dimensional systems is studied by combining the braid group formalism with a gauge invariance analysis. We show that flux insertions (or large gauge transformations) pertinent to the toroidal topology induce…
In this paper, we study group equations with occurrences of automorphisms. We describe equational domains in this class of equations. Moreover, we solve a number of open problem posed in universal algebraic geometry.
We define invariants of words in arbitrary groups, measuring how letters in a word are interleaving, perfectly detecting the dimension series of a group. These are the letter-braiding invariants. On free groups, braiding invariants coincide…
We provide two alternative ways to determine the number of (bi-)twisted conjugacy classes in a finite group: one by counting certain irreducible characters and one by counting certain twisted conjugacy classes of other endomorphisms. In…
Equivariant T-duality triples of locally compact abelian groups are considered. The motivating example dealing with the group $\R^n$ containing a lattice $\Z^n$ comes with an isomorphism in twisted equivariant K-theory.