Foundations of Topological Stacks I

Simple item page
dc.creatorNoohi, Behrang
dc.date2005-03-13
dc.date.accessioned2026-07-07T05:17:55Z
dc.date.available2026-07-07T05:17:55Z
dc.descriptionThis is the first in a series of papers devoted to foundations of topological stacks. We begin developing a homotopy theory for topological stacks along the lines of classical homotopy theory of topological spaces. In this paper we go as far as introducing the homotopy groups and establishing their basic properties. We also develop a Galois theory of covering spaces for a (locally connected semilocally 1-connected) topological stack. Built into the Galois theory is a method for determining the stacky structure (i.e., inertia groups) of covering stacks. As a consequence, we get for free a characterization of topological stacks that are quotients of topological spaces by discrete group actions. For example, this give a handy characterization of good orbifolds. Orbifolds, graphs of groups, and complexes of groups are examples of topological (Deligne-Mumford) stacks. We also show that any algebraic stack (of finite type over $\mathbb{C}$) gives rise to a topological stack. We also prove a Riemann Existence Theorem for stacks. In particular, the algebraic fundamental group of an algebraic stack over $\mathbb{C}$ is isomorphic to the profinite completion of the fundamental group of its underlying topological stack. The next paper in the series concerns function stacks (in particular loop stacks) and fibrations of topological stacks. This is the first in a series of papers devoted to foundations of topological stacks.
dc.description81 pages
dc.identifierhttps://arxiv.org/abs/math/0503247
dc.identifierhttp://arxiv.org/abs/math/0503247
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74477
dc.subjectAlgebraic Geometry
dc.subjectAlgebraic Topology
dc.subject22A22, 14A20, 58A03, 58H05
dc.titleFoundations of Topological Stacks I
dc.typetext

Files

Collections

arXiv