Infinite Noncommutative Covering Projections
arXiv:1405.1859
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 devoted to the noncommutative generalization of infinite covering projections. Infinite covering projections of spectral triples are also discussed. It is shown that covering projection of foliation algebras can be constructed by topological coverings of foliations and isospectral deformations. Described an interrelationship between noncommutative covering projections and -homology. The Dixmier trace of noncommutative covering projections is discussed.
51 pages, 34 references. arXiv admin note: text overlap with arXiv:hep-th/9904001, arXiv:1107.3458, arXiv:math/0608572 by other authors. text overlap with arXiv:math/0011194, arXiv:1107.3458 by other authors