Stephen Theriault

Homotopy theory of Poincare Duality complexes

Poincare Duality complexes are CW-complexes whose cap product satisfies Poincare Duality. They are topological generalizations of manifolds. We will use methods from homotopy theory to determine information about the homotopy types of interesting families of Poincare Duality complexes and their based loop spaces. In particular, this gives incisive insight into properties of their homotopy groups that positively supports major conjectures posed more broadly about CW-complexes.