Introduction to Topological Stacks

Short Course

Introduction to Topological Stacks

Behrang Noohi

(Max Planck Institute, Bonn)

June 26-28, 2006

Abstract: In these lectures we will introduce topological stacks and explain how classical homotopy theory can be extended to the setting of topological stacks. We motivate this by showing that each of the following classes of objects naturally gives rise to a class of topological stacks:

orbifolds
graphs of groups and, more generally, complexes of groups,
Artin stacks over the complex numbers,
Topological spaces with a group action,
Differential groupoids,
Foliated manifolds

In particular, homotopy theory of topological stacks can be applied in all these situations in a unified manner. We show how certain general results about topological stacks specialize to well-known or new, results in each of these theories.

References:
Foundations of Topological Stacks I by Behrang Noohi
A homotopy theory for stacks by Sharon Hollander
Introduction to Stacks (Introduction to a book in preparation) by William Fulton et al.

Schedule:
Monday 26: 10h30-12h, Room 3.10
Tuesday 27: 10h30-12h, Room 3.10
Wednesday 28: 10h30-12h, Room 3.10.

Introductory lecture (Gustavo Granja)
Friday 23: 16h30-18h, Room 4.35
The aim of this lecture will be to introduce and give examples of Grothendieck topologies, sheaves, and some categorical constructions needed in the course.

Departamento de Matemática
Instituto Superior Técnico

Support:
Project "Homotopy Theoretic Methods in Geometry and Algebra ", (PDCT/MAT/58497/2004).
Project "Symplectic Topology and Affine Geometries", (POCI/MAT/57888/2004).
Centro de Análise Matemática, Geometria e Sistemas Dinâmicos

Organization: Gustavo Granja