Quantization of branched coverings
Operator Algebras
2015-05-18 v2 General Topology
Geometric Topology
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.
Cite
@article{arxiv.1002.3491,
title = {Quantization of branched coverings},
author = {Alexander Pavlov and Evgenij Troitsky},
journal= {arXiv preprint arXiv:1002.3491},
year = {2015}
}
Comments
v2:Small changes in examples and references. Submitted.