Cohomology and $K$-theory rings of the space of commuting elements in $SU(2)$
Abstract
In this paper, we compute explicitly both the $K$-theory and integral cohomology rings of the space of commuting elements in $SU(2)$ via the $K$-theory of its desingularization. We also briefly discuss the different behavior of its cohomology with complex and $\mathbb{Z}_2$ coefficients in the context of representation stability and FI-modules.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2022
- DOI:
- 10.48550/arXiv.2211.13850
- arXiv:
- arXiv:2211.13850
- Bibcode:
- 2022arXiv221113850F
- Keywords:
-
- Mathematics - Algebraic Topology;
- Mathematics - K-Theory and Homology;
- 55N20;
- 55N15
- E-Print:
- 27 pages. Accepted by Homology, Homotopy and Applications