Index estimate by first Betti number of minimal hypersurfaces in compact symmetric spaces

Abstract

We show that the Morse index of unstable closed minimal hypersurface $\Sigma$ in a compact semi-simple Riemannian symmetric space $M=G/K$ is bounded from below by constant times the first Betti number of $\Sigma$. Our proof is based on a natural extension of the previous method and this also provides a novel approach for the index estimate.