The purpose of this paper1 is to determine the cohomology algebra of a loop space over a topological space whose cohomology algebra is a truncated polynomial algebra generated by an element of even degree. As special cases we obtain the well-known results when the base space has as cohomology algebra an exterior algebra (the base space an even dimensional sphere) or a polynomial algebra (the ba...

In this paper we address Fano foliations on complex projective varieties. These are foliations F whose anti-canonical class −KF is ample. We focus our attention on a special class of Fano foliations, namely del Pezzo foliations on complex projective manifolds. We show that these foliations are algebraically integrable, with one exceptional case when the ambient space is Pn. We also provide a cl...