The first and second widths of the real projective space

Abstract

In this paper, we deal with the first and second widths of the real projective space R P n \mathbb {RP}^{n} , for n n ranging from 4 4 to 7 7 , and for this we used some tools from the Almgren-Pitts min-max theory. In a recent paper, Ramirez-Luna computed the first width of the real projective spaces, and, at the same time, we obtained optimal sweepouts realizing the first and second widths of those spaces.