Generalizations of intersection homology with duality over the integers

Greg Friedman

Published 2016-12-30Version 1

We provide a generalization of the Deligne sheaf construction of intersection homology theory and a corresponding generalization of Poincare duality on pseudomanifolds such that the Goresky-MacPherson, Goresky-Siegel, and Cappell-Shaneson duality theorems all arise as special cases. Unlike classical intersection homology theory, our duality theorem holds with ground coefficients in an arbitrary PID and with no "locally torsion free" conditions on the underlying space.