Index bounds for minimal hypersurfaces of the sphere Alessandro Savo 58J5053C42minimal hypersurfacesindexfirst Betti number We consider a compact, orientable minimal hypersurfaces of the unit sphere and prove a comparison theorem between the spectrum of the stability operator and that of the Laplacian on $1$-forms. As a corollary, we show that the index is bounded below by a linear function of the first Betti number; in particular, if the first Betti number is large, then the immersion is highly unstable. Indiana University Mathematics Journal 2010 text pdf 10.1512/iumj.2010.59.4013 10.1512/iumj.2010.59.4013 en Indiana Univ. Math. J. 59 (2010) 823 - 838 state-of-the-art mathematics http://iumj.org/access/