Long & Medium-Term Research: Qualitatively Riemannian Foliations. This award recommendation is made under the Program for Long & Medium-Term Research at Foreign Centers of Excellence. The program seeks to enable U.S. scientists and engineers to conduct long-term research abroad at research institutions of proven excellence. Awards provide opportunities for the conduct of joint research, and the use of unique or complimentary facilities, expertise and experimental conditions in foreign countries. This award will support an 18-month visit by Dr. Mark Kellum to work with Professor Etienne Ghys of L' cole Normale Sup rieure de Lyon in Lyon, France, on "Qualitatively Riemannian Foliations." The proposal concerns ongoing research into the structure of qualitatively Riemannian foliations on compact manifolds, a continuation of research the principal investigator began with his thesis, where he showed that the Molino theory on leaf closures in Riemannian foliations generalizes to the qualitatively Riemannian situation. In his thesis, he employed the theory of locally compact transformation groups. This theory, together with results due to Sacksteder, Furstenberg and Ellis in measure- theoretic and topological dynamics, suggests studying the closure of the holonomy pesudogroup, when it consists of equicontinuous or distal local homeomorphisms. These theories also suggest a relaxation of our original differentiability assumptions on the holonomy pseudogroup of local metric isometries. Ghys also points to many of the same results in his treatment of qualitatively Riemannian foliations.
