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We show that there is a homotopy cofiber sequence of spectra relatingCarlsson's deformation K-theory of a group G to its "deformation representationring," analogous to the Bott periodicity sequence relating connective K-theoryto ordinary homology. We then apply this to study simultaneous similarity ofunitary matrices.

The Bott cofiber sequence in deformation K-theory and simultaneous similarity in U(n)