Strong multiplicity one theorems and homological min-max theory

Abstract

It was asked by Marques-Neves which min-max $p$-widths of the unit $3$-sphere lie strictly between $2{\pi }^2$ and $8\pi$. We show that the 10th to the 13th widths do. More generally, we prove stronger versions of X. Zhou's multiplicity one theorem.

arXiv commentv3: slight improve of main results; to appear in Adv. Math