Connes defined a noncommutative analog of a closed oriented Riemannian spin^c manifold using spectral triples. Using his definition it is unclear how to separate the smooth structure from the metric. ...
Consider the spinc structure on the flat standard 3-torus, which you get from the trivial (or any other) spin structure. Its associated vector bundle can be identified with a trivial bundle with fibre ...
Basically, I am trying to build explicit examples of Dirac operators. To this end, I'm looking at the surface E = C/(Z + λZ) - for some λ in H \ SL(2,Z) - with the Euclidean metric and ...
Background Let $M$ be a spin manifold and let $\Gamma$ be a finite group acting freely and isometrically on $M$ in such a way that $M/\Gamma$ is a smooth riemannian manifold. The quotient will be ...