Coverings in Noncommutative Geometry
Conference Proceeding: 01/2008; In proceeding of: International conference on Di�erential Equations and Topology, Moscow, http://pont2008.cs.msu.ru/en, At http://www.mathframe.com/articles/noncommutative/conjecture2.pdf
Abstract
generalization of Riemann manifold, or, in other words, a
quantization of a Riemannian manifold. The idea is follows:
Having a Riemann manifold M, one may consider an algebra of
smooth functions on M. This algebra is, obviously, commutative.
Roughly speaking, Alain Connes suggested to consider a case when
a commutative algebra is replaced by a noncommutative one,
preserving the main properties of manifolds.
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