  By considering a (not necessarily locally-flat) PL knot as the singular locus
of a PL stratified pseudomanifold, we can use intersection homology theory to
define intersection Alexander polynomials, a generalization of the classical
Alexander polynomial invariants for smooth or PL locally-flat knots. We show
that the intersection Alexander polynomials satisfy certain duality and
normalization conditions analogous to those of ordinary Alexander polynomials,
and we explore the relationships between the intersection Alexander polynomials
and certain generalizations of the classical Alexander polynomials that are
defined for non-locally-flat knots. We also investigate the relations between
the intersection Alexander polynomials of a knot and the intersection and
classical Alexander polynomials of the link knots around the singular strata.
To facilitate some of these investigations, we introduce spectral sequences for
the computation of the intersection homology of certain stratified bundles.

Geometric Topology;Algebraic Topology