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Singularity structures for noncommutative spaces


Authors: Shantanu Dave and Michael Kunzinger
Journal: Trans. Amer. Math. Soc. 367 (2015), 251-273
MSC (2010): Primary 58J40; Secondary 58J47, 58J42
DOI: https://doi.org/10.1090/S0002-9947-2014-06024-8
Published electronically: June 27, 2014
MathSciNet review: 3271260
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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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Additional Information

Shantanu Dave
Affiliation: Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Vienna, Austria
Email: shantanu.dave@univie.ac.at

Michael Kunzinger
Affiliation: Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Vienna, Austria
Email: michael.kunzinger@univie.ac.at

DOI: https://doi.org/10.1090/S0002-9947-2014-06024-8
Received by editor(s): June 13, 2012
Received by editor(s) in revised form: November 14, 2012
Published electronically: June 27, 2014
Additional Notes: The first author was supported by FWF grants P20525 and P24420 of the Austrian Science Fund
The second author was supported by FWF grants Y237-N13 and P20525 of the Austrian Science Fund
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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