On globally non-trivial almost-commutative manifolds

Abstract

Within the framework of Connes' noncommutative geometry, we define and study globally non-trivial (or topologically non-trivial) almost-commutative manifolds. In particular, we focus on those almost-commutative manifolds that lead to a description of a (classical) gauge theory on the underlying base manifold. Such an almost-commutative manifold is described in terms of a 'principal module', which we build from a principal fibre bundle and a finite spectral triple. We also define the purely algebraic notion of 'gauge modules', and show that this yields a proper subclass of the principal modules. We describe how a principal module leads to the description of a gauge theory, and we provide two basic yet illustrative examples.

34 pages, minor revisions

References in corpus (4)

• Noncommutative Geometry and the standard model with neutrino mixing
• Resilience of the Spectral Standard Model
• Particle Physics from Almost Commutative Spacetimes
• The noncommutative geometry of Yang-Mills fields

Cited by in corpus (1)

• Spectral interactions between strings in the Higgs background