Semicoverings: a generalization of covering space theory

@article{Brazas2011SemicoveringsAG,
  title={Semicoverings: a generalization of covering space theory},
  author={Jeremy Brazas},
  journal={arXiv: Algebraic Topology},
  year={2011}
}
  • Jeremy Brazas
  • Published 15 August 2011
  • Mathematics
  • arXiv: Algebraic Topology
The fundamental groupoid of a space becomes enriched over the category of topological spaces when the hom-sets are endowed with topologies intimately related to universal constructions of topological groups. This paper is devoted to a generalization of classical covering theory in the context of this construction. 

Figures from this paper

GENERALIZED COVERING SPACES AND THE GALOIS FUNDAMENTAL GROUP
We introduce a functor π 1 from the category of based, connected, locally path connected spaces to the category of complete topological groups. We then compare this groups to the fundamental group.Expand
Open subgroups of free topological groups
The theory of covering spaces is often used to prove the Nielsen-Schreier theorem, which states that every subgroup of a free group is free. We apply the more general theory of semicovering spaces toExpand
On category of co-coverings
In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for theExpand
On Relationship Between Generalized Covering Subgroups of Fundamental Groups
In this talk we are interested to focus on subgroups of topologized fundamental groups and some relationships between generalized covering subgroups and some famous subgroups of the fundamental groupExpand
On Subgroups of Topologized Fundamental Groups and Generalized Coverings
In this paper, we are interested in study subgroups of topologized fundamental groups and their influences on generalized covering maps. More precisely, we find some relationships between generalizedExpand
On Open Subgroups of Topologized Fundamental Group
In this talk we are interested to focus on open subgroups of topologized fundamental groups and give some equivalent conditions on a topological space to make sure a subgroup of its topologizedExpand
When is a Local Homeomorphism a Semicovering Map?
In this paper, by reviewing the concept of semicovering maps, we present some conditions under which a local homeomorphism becomes a semicovering map. We also obtain some conditions under which aExpand
Fundamental groups of locally connected subsets of the plane
We show that every homomorphism from a one-dimensional Peano continuum to a planar Peano continuum is induced by a continuous map up to conjugation. We then prove that the topological structure ofExpand
GENERALIZED COVERING SPACE THEORIES
In this paper, we unify various approaches to generalized covering space theory by introducing a categorical framework in which coverings are dened purely in terms of unique lifting properties. ForExpand
CJMS . xx ( x ) ( 201 x ) , xxxx On category of co-coverings
In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been developed for the coveringExpand
...
1
2
3
4
...

References

SHOWING 1-10 OF 23 REFERENCES
Discreteness and Homogeneity of the Topological Fundamental Group
For a locally path connected topological space, the topological fundamental group is discrete if and only if the space is semilocally simply-connected. While functoriality of the topologicalExpand
Compactly generated quasitopological homotopy groups with discontinuous multiplication
For each positive integer Q there exists a path connected metric compactum X such that the Qth-homotopy group of X is compactly generated but not a topological group (with the quotient topology).
Algebraic Topology
The focus of this paper is a proof of the Nielsen-Schreier Theorem, stating that every subgroup of a free group is free, using tools from algebraic topology.
Fundamental progroupoid and bundles with a structural category
Abstract In this paper, for a given space X , a structural category C , and a faithful functor η from C to the category of spaces, we introduce a notion of ( C , η)-bundle which contains asExpand
Theory of covering spaces
Introduction. In this paper I study covering spaces in which the base space is an arbitrary topological space. No use is made of arcs and no assumptions of a global or local nature are required. InExpand
The fundamental group as a topological group
Abstract This paper is devoted to the study of a natural group topology on the fundamental group which remembers local properties of spaces forgotten by covering space theory and weak homotopy type.Expand
Multiplication is discontinuous in the Hawaiian earring group (with the quotient topology)
The natural quotient map q from the space of based loops in the Hawaiian earring onto the fundamental group provides a new example of a quotient map such that q x q fails to be a quotient map. ThisExpand
The topological fundamental group and free topological groups
Abstract The topological fundamental group π 1 top is a homotopy invariant finer than the usual fundamental group. It assigns to each space a quasitopological group and is discrete on spaces whichExpand
Fundamental pro-groupoids and covering projections
We introduce a new notion of covering projection E → X of a topological spaceX which reduces to the usual notion ifX is locally connected. We use locally constant presheaves and covering reducedExpand
Covering maps for locally path-connected spaces
We define Peano covering maps and prove basic properties analogous to classical covers. Their domain is always locally path-connected but the range may be an arbitrary topological space. One ofExpand
...
1
2
3
...