The Noncommutative Geometry Generalization of Fundamental Group

2006/04/24 by Ivankov, Petr R., Ivankov, Nickolay P.
#Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT) #m3dcs

paper · doi:10.48550/arxiv.math/0604508

Abstract

A notion of fundamental group of spectral triples has been introduced. The notion uses a noncommutative analogue of unramified coverings. It was shown that in commutative case this fundamental group is a profinite completion of fundamental group of corresponding Riemann manifold.

Related

• Coverings of Spectral Triples
• An Introduction to Noncommutative Geometry
• Inverse Limits of Spectral Triples
• The fundamental group of a noncommutative space
• Unoriented Spectral Triples