We construct, for and , closed manifolds with finite nonzero ), where denotes the minimum number of critical points of a smooth map . We also give some explicit families of examples for even and , taking advantage of the Lie group structure on . Moreover, there are infinitely many such examples with . Eventually, we compute the signature of the manifolds occurring for even .
"Manifolds Which Admit Maps with Finitely Many Critical Points Into Spheres of Small Dimensions." Michigan Math. J. 67 (3) 585 - 615, August 2018. https://doi.org/10.1307/mmj/1529460326