Configuration spaces of commuting elements
Abstract
In this article, we introduce the space of configurations of commuting elements in a topological group and show that it satisfies rational homological stability for the sequences of unitary, special unitary, and symplectic groups. In the case of a finite product of such groups, we also prove that it satisfies cohomological rational representation stability with respect to the number of elements in the tuple if the rank of the product is at least two and cohomological rational stability for the space of unordered configurations of commuting elements without restriction on the rank. Finally, we present some computations of cohomology in the unstable range.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Geometric and Algebraic Topology
Advanced Algebra and Geometry
Publication details
- Journal / source
- Kyoto journal of mathematics
- Volume
- 66
- Issue
- 2
- Pages
- 253–279
- Publication date
- 16 January 2026
- Language
- EN