Inverse Limits of Spectral Triples

Abstract

Gelfand - Naĭmark theorem supplies a one to one correspondence between commutative $C^{\ast }$-algebras and locally compact Hausdorff spaces. So any noncommutative $C^{\ast }$-algebra can be regarded as a generalization of a topological space. Similarly a spectral triple is a generalization of a Riemannian manifold. An (infinitely listed) covering of a Riemannian manifold has natural structure of Riemannian manifold. Here we will consider the noncommutative generalization of this result.

80 pages, 37 references

References in corpus (2)

• Gravity coupled with matter and foundation of non-commutative geometry
• The Standard Model a la Connes-Lott