## 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.## References

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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