Commuting matrices and Atiyah's Real K-theory

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We describe the C2-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.
Original languageEnglish
JournalJournal of Topology
Volume12
Issue number3
Pages (from-to)833-854
ISSN1753-8416
DOIs
Publication statusPublished - 2019

ID: 211219237