The algebraic-to-topological hermitian K-theory conjecture for Banach algebras

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Let AA be a real or complex commutative Banach algebra with involution, let ε\varepsilon denote the hermitian sign, and let mm be the coefficient modulus. The algebraic-to-topological hermitian K-theory conjecture. The natural map

εKQialg(A;Z/m)⟶εKQitop(A;Z/m){}_{\varepsilon}KQ_{i}^{\mathrm{alg}}(A;\mathbb{Z}/m)\longrightarrow{}_{\varepsilon}KQ_{i}^{\mathrm{top}}(A;\mathbb{Z}/m)

is an isomorphism for i≥1i\geq1. This is the hermitian analogue of the stated algebraic-to-topological comparison theorem for ordinary KK-theory; the supplied text does not report a resolution.

References

Primary source

A. J. Berrick, M. Karoubi and P. A. Østvær, “Periodicity of hermitian K-groups”, arXiv:1101.2056 (2011).

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