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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Spectral geometries on a compact metric space

Author: S. Buyalo
Translated by: the author
Original publication: Algebra i Analiz, tom 30 (2018), nomer 5.
Journal: St. Petersburg Math. J. 30 (2019), 821-839
MSC (2010): Primary 51K10
Published electronically: July 26, 2019
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Abstract: The notion of a spectral geometry on a compact metric space $ X$ is introduced. This is a sort of discrete approximation of $ X$ motivated by the notion of a spectral triple from noncommutative geometry. A set of axioms characterizing spectral geometries is given. Bounded deformations of spectral geometries are studied and the relationship between the dimension of a spectral geometry and more traditional dimensions of metric spaces is investigated.

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Additional Information

S. Buyalo
Affiliation: St. Petersburg Branch Steklov Mathematical Institute, 27 Fontanka, 191023 St. Petersburg, Russia

Keywords: Dimension, Connes metric, bounded deformation, Dirac operator
Received by editor(s): June 1, 2018
Published electronically: July 26, 2019
Additional Notes: This work is supported by the Program of the Presidium of the Russian Academy of Sciences no. 01 “Fundamental Mathematics and its Applications” under Grant PRAS-18-01
Article copyright: © Copyright 2019 American Mathematical Society