Global algebraic \(K\)-theory. (English) Zbl 1520.19003
Summary: We introduce a global equivariant refinement of algebraic \(K\)-theory; here ‘global equivariant’ refers to simultaneous and compatible actions of all finite groups. Our construction turns a specific kind of categorical input data into a global \(\Omega\)-spectrum that keeps track of genuine \(G\)-equivariant infinite loop spaces, for all finite groups \(G\). The resulting global algebraic \(K\)-theory spectrum is a rigid way of packaging the representation K-theory, or ‘Swan \(K\)-theory’ into one highly structured object.
{© 2022 The Authors. Journal of Topology is copyright © London Mathematical Society.}
{© 2022 The Authors. Journal of Topology is copyright © London Mathematical Society.}
MSC:
| 19D23 | Symmetric monoidal categories |
| 18F25 | Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) |
| 55P48 | Loop space machines and operads in algebraic topology |
| 55P91 | Equivariant homotopy theory in algebraic topology |
| 55Q91 | Equivariant homotopy groups |
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