Min-max widths of the real projective 3-space

Batista, Márcio; Lima, Anderson

doi:10.1090/tran/8682

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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