Quantization of branched coverings

Abstract

We identify branched coverings (continuous open surjections p:Y->X of Hausdorff spaces with uniformly bounded number of pre-images) with Hilbert C*-modules C(Y) over C(X) and with faithful unital positive conditional expectations E:C(Y)->C(X) topologically of index-finite type. The case of non-branched coverings corresponds to projective finitely generated modules and expectations (algebraically) of index-finite type. This allows to define non-commutative analogues of (branched) coverings.

v2:Small changes in examples and references. Submitted.

References in corpus (1)

• A module frame concept for Hilbert C*-modules

Cited by in corpus (3)

• Adjoint functors between categories of Hilbert C*-modules
• Wieler solenoids, Cuntz-Pimsner algebras and K-theory
• Frobenius structures over Hilbert C*-modules