Noncommutative Local Systems
arXiv:1411.2505 · doi:10.13140/2.1.2479.8403
Abstract
Gelfand - Naĭmark theorem supplies a one to one correspondence between commutative -algebras and locally compact Hausdorff spaces. So any noncommutative -algebra can be regarded as a generalization of a topological space. Generalizations of several topological invariants may be defined by algebraic methods. For example Serre Swan theorem states that complex topological -theory coincides with -theory of -algebras. This article is concerned with generalization of local systems. The classical construction of local system implies an existence of a path groupoid. However the noncommutative geometry does not contain this object. There is a construction of local system which uses covering projections. Otherwise a classical (commutative) notion of a covering projection has a noncommutative generalization. A generalization of noncommutative covering projections supplies a generalization of local systems.
17 pages, 26 references. arXiv admin note: substantial text overlap with arXiv:1405.1859, arXiv:1408.5813