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Proceedings of the American Mathematical Society

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Graded topological spaces


Author: Clemens Koppensteiner
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 54B40, 18F20; Secondary 55M05
DOI: https://doi.org/10.1090/proc/14867
Published electronically: December 6, 2019
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Abstract: We introduce the notion of a ``graded topological space'': a topological space endowed with a sheaf of abelian groups which we think of as a sheaf of gradings. Any object living on a graded topological space will be graded by this sheaf of abelian groups. We work out the fundamentals of sheaf theory and Poincaré-Verdier duality for such spaces.


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Additional Information

Clemens Koppensteiner
Affiliation: Institute for Advanced Study, 1 Einstein Drive, Princeton, New Jersey 08540
Address at time of publication: Mathematical Institute, University of Oxford, Andrew Wiles Building, Oxford, OX2 6GG, United Kingdom
Email: clemens.koppensteiner@maths.ox.ac.uk

DOI: https://doi.org/10.1090/proc/14867
Received by editor(s): July 1, 2019
Published electronically: December 6, 2019
Additional Notes: The author was supported by the National Science Foundation under Grant No. DMS-1638352.
Communicated by: Alexander Braverman
Article copyright: © Copyright 2019 American Mathematical Society