Topological groupoids with involution and real algebraic stacks
Abstract
Abstract To a topological groupoid endowed with an involution, we associate a topological groupoid of fixed points, generalizing the fixed-point subspace of a topological space with involution. We prove that when the topological groupoid with involution arises from a Deligne-Mumford stack over $$ \mathbb {R} $$ R , this fixed locus coincides with the real locus of the stack. This provides a topological framework to study real algebraic stacks, and in particular real moduli spaces. Finally, we propose a Smith–Thom type conjecture in this setting, generalizing the Smith–Thom inequality for topological spaces endowed with an involution.
Fields of Study & Subjects
Fuzzy and Soft Set Theory
Homotopy and Cohomology in Algebraic Topology
Constraint Satisfaction and Optimization
Publication details
- Journal / source
- manuscripta mathematica
- Publisher
- Springer Science and Business Media LLC
- Volume
- 177
- Issue
- 4
- Pages
- 47–47
- Publication date
- 26 June 2026
- Language
- EN