Osman Mucuk

Covering groups of non-connected topological groups revisited

In general a universal covering of a non connected topological group need not admit a topological group structure such that the covering map is a morphism of topological groups. This result is due to R.L. Taylor (1953). We generalise this result and relate it to the theory of obstructions to group extensions. The methods use: the equivalence between covering maps of X and covering groupoids of the fundamental groupoid of X; the equivalence between group groupoids and crossed modules; and descriptions of cohomology in terms of crossed complexes.

Coverings of internal groupoids and crossed modules in the category of groups with operations

Abstract. In this paper we prove some results on the covering morphisms of internal groupoids. We also give a result on the coverings of the crossed modules of groups with operations.

Coverings and crossed modules of topological groups with operations

It is a well known result in the covering groups that a subgroup

Normality and Quotients in Crossed Modules and Group-groupoids

G

Group-groupoids and monodromy groupoids

of the fundamental group at the identity of a semi-locally simply connected topological group determines a covering morphism of topological groups with characteristic group

Local subgroupoids II: Examples and properties

G

G-sequentially connectedness for topological groups with operations

. In this paper we generalize this result to a large class of algebraic objects called topological groups with operations, including topological groups. We also give the cover of crossed modules within topological groups with operations.

Coverings of topological semi-abelian algebras

We consider the important equivalence between crossed modules and group-groupoids, and show how normality and quotient concepts are related in these two categories.

Extendibility, monodromy, and local triviality for topological groupoids

Abstract This paper gives an introduction to some results on monodromy groupoids and the monodromy principle, and then develops the notion of monodromy groupoid for group groupoids.

Group-groupoid actions and liftings of crossed modules

Abstract The notion of local subgroupoid as a generalisation of a local equivalence relation was defined in a previous paper by the first two authors. Here we use the notion of star path connectivity for a Lie groupoid to give an important new class of examples, generalising the local equivalence relation of a foliation, and develop in this new context basic properties of coherence, due earlier to Rosenthal in the special case. These results are required for further applications to holonomy and monodromy.