Related papers: Group-groupoids and monodromy groupoids
In a previous paper, we introduce and study formal manifolds, which generalize smooth manifolds. In this paper, we establish the basic theory of formal Lie groups, which are group objects in the category of formal manifolds. In particular,…
Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B contained in A which is embedded with a stronger structure S. These types of structures occurin our…
This short paper focuses on Schr\"oder's contribute towards a structural view of group theory.
A cohomology theory for lambda-rings is developed. This is then applied to study deformations of lambda-rings.
In this article, the ring of polynomials is studied in a systematic way through the theory of monoid rings. As a consequence, this study provides natural and canonical approaches in order to find easy and rigorous proofs and methods for…
A survey of recent results about profinite groups, and results about infinite and finite groups where the theory of profinite groups plays a leading role.
The paper gives a short account of the contents of "Regular Algebraic K-Theory For Groups" by the author and its connections with other homology and K-theories.
In this survey article we introduce the notion of frontals, which provides a class of generalised submanifolds with singularities but with well-defined tangent spaces. We present a review of basic theory and known studies on frontals in…
In this paper, we study connections between the structure of a group and the structure of the group (under pointwise product) of its polynomial functions.
We give a rather general construction of double categories and so, under further conditions, double groupoids, from a structure we call a `double module'. We also give a homotopical construction of a double groupoid from a triad consisting…
In the spirit of Conway we define a groupoid starting from projective planes of order $q$, where $q$ is odd. The associated group of these groupoids is then investigated.
We study monodromy groups of elliptic fibrations over the projective line.
In this paper, we state and prove precise theorems on the classification of the category of (braided) categorical groups and their (braided) monoidal functors, and some applications obtained from the basic studies on monoidal functors…
We investigate monodromy groups arising in enumerative geometry, with a particular focus on how these groups are influenced by prescribed symmetries. To study these phenomena effectively, we work in the framework of moduli stacks rather…
We describe the iterated monodromy groups associated with post-critically finite quadratic polynomials, and explicit their connection to the `kneading sequence' of the polynomial. We then give recursive presentations by generators and…
This thesis is about the study of Lie groupoids endowed with a compatible (multiplicative) differential 1-form. The motivation and scope of the present work is to study the geometry of PDEs using the formalism of Lie groupoids and…
We show a classification method for finite groupoids and discuss the cardinality of cosets and its relation with the index. We prove a generalization of the Lagrange's Theorem and establish a Sylow theory for groupoids.
We study and give examples of braided groupoids, and, a fortiori, non-degenerate solutions of the quiver-theoretical braid equation.
This is an account of the theory of inverse semigroups, assuming only that the reader knows the basics of semigroup theory.
When G is a finite abelian group, we define G-spans of groupoids and their associated matrices with entries in the group ring QG and show that composition of spans corresponds to multiplication of matrices.