Editing Singularity theory (section)

===Duality===
An important reason why singularities cause problems in mathematics is that, with a failure of manifold structure, the invocation of [[Poincaré duality]] is also disallowed. A major advance was the introduction of [[intersection cohomology]], which arose initially from attempts to restore duality by use of strata. Numerous connections and applications stemmed from the original idea, for example the concept of [[perverse sheaf]] in [[homological algebra]].