"The loop space homotopy type of simply-connected four-manifolds" by Stephen Theriault (University of Souphamton)

Abstract:

Abstract: We determine the integral homotopy type of the based loop space of a simply-connected four-manifold. This turns out to depend only on the rank of the degree 2 cohomology of the manifold. The decompositions are obtained as special cases of more general loop space decompositions of certain torsion-free CW-complexes with well-behaved skeleta and some Poincare duality features. This is joint work with Piotr Beben.