Finite closed coverings of compact quantum spaces
Abstract
We show that a projective space P^\infty(Z/2) endowed with the Alexandrov topology is a classifying space for finite closed coverings of compact quantum spaces in the sense that any such a covering is functorially equivalent to a sheaf over this projective space. In technical terms, we prove that the category of finitely supported flabby sheaves of algebras is equivalent to the category of algebras with a finite set of ideals that intersect to zero and generate a distributive lattice. In particular, the Gelfand transform allows us to view finite closed coverings of compact Hausdorff spaces as flabby sheaves of commutative C*-algebras over P^\infty(Z/2).
Cite
@article{arxiv.0901.0074,
title = {Finite closed coverings of compact quantum spaces},
author = {Piotr M. Hajac and Atabey Kaygun and Bartosz Zielinski},
journal= {arXiv preprint arXiv:0901.0074},
year = {2012}
}
Comments
26 pages, the Teoplitz quantum projective space removed to another paper. This is the third version which differs from the second one by fine tuning and removal of typos