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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Min-max widths of the real projective 3-space
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by Márcio Batista and Anderson Lima PDF
Trans. Amer. Math. Soc. 375 (2022), 5239-5258 Request permission

Abstract:

In this paper we deal with the min-max invariant known as $p$-width for the 3-dimensional real projective space. More precisely, we present an explicit and sharp $p$-sweepout, for $p=1$, $2$, $3$, and compute the value of the $p$-width for such values. Using Lusternik-Schnirelmann type argument we also verify the jump of the $5$-width and, using algebraic sets, we estimate the $9$-width.
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Additional Information
  • Márcio Batista
  • Affiliation: CPMAT - IM, Universidade Federal de Alagoas, Maceió, AL, 57072-970, Brazil
  • MR Author ID: 916216
  • ORCID: 0000-0002-6495-3842
  • Email: mhbs@mat.ufal.br
  • Anderson Lima
  • Affiliation: CPMAT - IM, Universidade Federal de Alagoas, Maceió, AL, 57072-970, Brazil
  • Email: jose.lima@im.ufal.br
  • Received by editor(s): July 29, 2021
  • Received by editor(s) in revised form: January 5, 2022, and January 25, 2022
  • Published electronically: April 21, 2022
  • Additional Notes: The first author is the corresponding author.
    This work was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico Grant: 308440/2021-8 to M.B. (CNPq) and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil.
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 5239-5258
  • MSC (2020): Primary 53C42, 53C23; Secondary 58J50
  • DOI: https://doi.org/10.1090/tran/8682
  • MathSciNet review: 4439504