St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

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

The 2024 MCQ for St. Petersburg Mathematical Journal is 0.68.

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Spectral geometries on a compact metric space
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by S. Buyalo
Translated by: the author
St. Petersburg Math. J. 30 (2019), 821-839
DOI: https://doi.org/10.1090/spmj/1571
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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Bibliographic Information
  • S. Buyalo
  • Affiliation: St. Petersburg Branch Steklov Mathematical Institute, 27 Fontanka, 191023 St. Petersburg, Russia
  • Email: sbuyalo@pdmi.ras.ru
  • 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
  • © Copyright 2019 American Mathematical Society
  • Journal: St. Petersburg Math. J. 30 (2019), 821-839
  • MSC (2010): Primary 51K10
  • DOI: https://doi.org/10.1090/spmj/1571
  • MathSciNet review: 3856102