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arXiv · 1405.5368

On globally non-trivial almost-commutative manifolds

Jord Boeijink·Koen van den Dungen
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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.

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Jord Boeijink, Koen van den Dungen. 2014-10-13. On globally non-trivial almost-commutative manifolds. https://doi.org/10.1063/1.4898769

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