Equivariant min-max hypersurface inG-manifolds with positive Ricci curvature

We consider a connected orientable closed Riemannian manifold M n+1 with positive Ricci curvature.Suppose G is a compact Lie group acting by isometries on M with 3 codim(G p) 7 for all p M. Then we show the equivariant min-max G-hypersurface corresponding to oneparameter G-sweepouts (of boundary-type) is a multiplicity one minimal G-hypersurface with a G-invariant unit normal and G-equivariant index one.As an application, we are able to establish a genus bound for , a control on the singular points of /G, and an upper bound for the (first) G-width of M provided n + 1 = 3 and the actions of G are orientation preserving.