Coverings of foliation algebras
Petr Ivankov

TL;DR
This paper explores the relationship between topological coverings of foliated manifolds and noncommutative coverings of their operator algebras, highlighting a natural but not bijective correspondence.
Contribution
It introduces a geometric construction linking topological and noncommutative coverings of foliations, clarifying the scope and limitations of this correspondence.
Findings
Established a natural correspondence between topological and noncommutative coverings.
Identified noncommutative coverings that do not fit the geometric construction.
Clarified the non-bijective nature of the relationship.
Abstract
This article is devoted to the geometric construction which states a natural correspondence between topological coverings of a foliated manifolds and noncommutative coverings of the operator algebras. However this correspondence is not one to one because there are noncommutaive coverings of foliations which do not comply with discussed in this article construction.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology
