Singularity structures for noncommutative spaces

Dave, Shantanu; Kunzinger, Michael

doi:10.1090/S0002-9947-2014-06024-8

Singularity structures for noncommutative spaces
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by Shantanu Dave and Michael Kunzinger PDF

Trans. Amer. Math. Soc. 367 (2015), 251-273 Request permission

Abstract:

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 propagation of singularities on a groupoid with that on the base manifold.

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