  Let M be a simply-connected closed Poincare Duality complex of dimension n.
Then M is obtained by attaching a cell of highest dimension to its
(n-1)-skeleton M'. Conditions are given for when the skeletal inclusion i:M'
--> M has the property that the based loops on i has a right homotopy inverse.
This is an integral version of the rational statement that such a right
homotopy inverse always exists provided the rational cohomology of M is not
generated by a single element. New methods are developed in order to do the
integral case. These lead to p-local versions and recover the full rational
statement. Families for which the integral statement holds include moment-angle
manifolds and quasi-toric manifolds.
