Coverings, correspondences, and noncommutative geometry

Details Coverings, correspondences, and noncommutative geometry Coverings, correspondences, and noncommutative geometry

2008-07-18

arxiv.org/abs/0807.2924v1

Physics

Mathematical Physics

31 pages, LaTeX

Scientific paper

10.1016/j.geomphys.2008.07.007

We construct an additive category where objects are embedded graphs in the 3-sphere and morphisms are geometric correspondences given by 3-manifolds realized in different ways as branched covers of the 3-sphere, up to branched cover cobordisms. We consider dynamical systems obtained from associated convolution algebras endowed with time evolutions defined in terms of the underlying geometries. We describe the relevance of our construction to the problem of spectral correspondences in noncommutative geometry.

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