Homotopy groups of highly connected Poincare duality complexes

Abstract: Methods are developed to relate the action of a principal fibration to relative Whitehead products in order to determine the homotopy type of certain spaces. The methods are applied to thoroughly analyze the homotopy type of the based loops on certain cell attachments. Key examples are (n-1)-connected Poincare Duality complexes of dimension 2n or 2n+1 with minor cohomological conditions.