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arXiv · 1807.06864

Commuting matrices and Atiyah's Real K-theory

Simon Gritschacher·Markus Hausmann
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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.

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Simon Gritschacher, Markus Hausmann. 2018-07-18. Commuting matrices and Atiyah's Real K-theory. https://doi.org/10.1112/topo.12104

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