Intersections of quadrics, moment-angle manifolds and connected sums

Abstract

The geometric topology of the generic intersection of two homogeneous coaxial quadrics in R was studied by the second author in [26] where it was shown that its intersection with the unit sphere is in most cases diffeomorphic to a triple product of spheres or to the connected sum of sphere products. The proof involved a geometric description of the group actions on them and of their polytope quotients as well as a splitting of the homology groups of those manifolds. It also relied heavily on a normal form for them and many related computations. The part about group actions, polytopes and homology splitting was equally valid for the intersection of any number of such