Commuting matrices and Atiyah's real K‐theory. Issue 3 (17th April 2019)

• Record Type: Journal Article
• Authors: Gritschacher, Simon; Hausmann, Markus
• Is Part Of: Journal of topology. Volume 12:Issue 3(2019)
• Page Start: 833
• Page End: 854
• Publication Date: 2019-04-17
• Subjects: 55N15 -- 55P42 -- 55P91 -- 55R35 (primary); Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12104
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract: We describe the C 2 ‐equivariant homotopy type of the space of commuting n ‐tuples in the stable unitary group in terms of Real K‐theory. The result is used to give a complete calculation of the homotopy groups of the space of commuting n ‐tuples in the stable orthogonal group, as well as of the coefficient ring for commutative orthogonal K‐theory.