Jim Davis

Conjecture: For any map from a closed 4-manifold E to a circle whose homotopy fiber has the homotopy type of a 3-manifold, there exists a fiber bundle over the circle with total space a 4-manifold homotopy equivalent to E. Theorem (joint with Shmuel...

Theorem: If a finite group G acts freely and homologically trivially on a finite complex K which has the homotopy type of a product of k-spheres, then G acts freely and homologically trivially on a product of (k+1)-spheres.