Singularity structures for noncommutative spaces

Details Singularity structures for noncommutative spaces Singularity structures for noncommutative spaces

2011-11-28

arxiv.org/abs/1111.6570v1

Mathematics

Functional Analysis

19 pages

Scientific paper

We introduce a (bi)category $\mathfrak{Sing}$ whose objects can be functorially assigned spaces of distributions and generalized functions. In addition, these spaces of distributions and generalized functions possess intrinsic notions of regularity and singularity analogous to usual Schwartz distributions on manifolds. The objects in this category can be obtained from smooth manifolds, noncommutative spaces, or Lie groupoids. An application of these structures relates the longitudinal propagation of singularities for pseudo-differential operators on a groupoid with propagation of singularities on the base manifold.

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