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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Bounded degree cosystolic expanders of every dimension
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by Shai Evra and Tali Kaufman
J. Amer. Math. Soc. 37 (2024), 39-68
DOI: https://doi.org/10.1090/jams/1019
Published electronically: July 21, 2023

Abstract:

In this work we present a new local to global criterion for proving a form of high dimensional expansion, which we term cosystolic expansion. Applying this criterion on Ramanujan complexes yields for every dimension an infinite family of bounded degree complexes with the topological overlap property. This answers an open question raised by Gromov.
References
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Bibliographic Information
  • Shai Evra
  • Affiliation: Einstein Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram, Jerusalem, 9190401, Israel
  • MR Author ID: 1144775
  • Email: shai.evra@mail.huji.ac.il
  • Tali Kaufman
  • Affiliation: Department of Computer Science, Bar-Ilan University, Ramat-Gan, 5290002, Israel
  • Email: kaufmant@mit.edu
  • Received by editor(s): March 19, 2018
  • Received by editor(s) in revised form: March 5, 2020, and June 6, 2022
  • Published electronically: July 21, 2023
  • Additional Notes: The first author’s research was supported in part by the ERC. The second author’s research was supported in part by the IRG, ERC and BSF.
  • © Copyright 2023 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 37 (2024), 39-68
  • MSC (2020): Primary 05C10, 55U10, 05C65, 53C23
  • DOI: https://doi.org/10.1090/jams/1019
  • MathSciNet review: 4654607