Related papers: Group-groupoids and monodromy groupoids

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…

In this course we introduce the main notions relative to the classical theory of modular forms. A complete treatise in a similar style can be found in the author's book joint with F. Str{\"o}mberg [1].

We propose and develop a theory that allows to characterize epimorphisms of profinite groups in terms of indecomposable epimorphisms.

Present notes can be viewed as an attempt to extend the notion of Schubert/Grothendieck polynomial to the context of an arbitrary algebraic oriented cohomology theory and, hence, of a commutative one-dimensional formal group law.

This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…

Groups, in which every subgroup containing some fixed primary cyclic subgroup has a complement, are investigated.

In this paper, we generalize the equivariant homotopy groups or equivalently the Rhodes groups. We establish a short exact sequence relating the generalized Rhodes groups and the generalized Fox homotopy groups and we introduce…

This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.

We study and develop a notion of isogeny for superstable groups. We prove several fundamental properties of the notion and then use it to formulate and prove uniqueness results. Connections to existing model theoretic notions are explained.

This should be the final version of this paper. Numberous minor improvements have been made to the manuscript, one argument has been corrected, and an appendix has been added.

We introduce the concept of monodromy coordinates for representing solutions to large polynomial systems. Representing solutions this way provides a time-memory trade-off in a monodromy solving algorithm. We describe an algorithm, which…

The main purpose of this paper is to introduce the structure of soft group category. In this category, we determine some special objects and morphisms having a universal structure such as the final object and product. Therefore, the…

This note gives an overview on the construction of symplectic groupoids as reduced phase spaces of Poisson sigma models and its generalization in the infinite dimensional setting (before reduction).

A Delta-groupoid is an algebraic structure which axiomatizes the combinatorics of a truncated tetrahedron. By considering two simplest examples coming from knot theory, we illustrate how can one associate a Delta-groupoid to an ideal…

The concept of Smarandache isotopy is introduced and its study is explored for Smarandache: groupoids, quasigroups and loops just like the study of isotopy theory was carried out for groupoids, quasigroups and loops. The exploration…

We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.

k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz-Krieger type. Here we develop a theory of the fundamental groupoid of a k-graph, and relate it…

We study the representation theory of the increasing monoid. Our results provide a fairly comprehensive picture of the representation category: for example, we describe the Grothendieck group (including the effective cone), classify…

In this paper, we extend the classical theory of crossed $G$-sets and the crossed Burnside ring from a finite group $G$ to a finite groupoid $\mathcal{G}$. We introduce a natural monoidal structure on the category of crossed…

This paper introduces a notion of fundamental group appropriate for laminations.