Singularity theory

For non-mathematical singularity theories, see singularity.

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.

Related Topics:
Poincaré duality - Intersection cohomology - Perverse sheaf - Homological algebra

~ ~ ~ ~ ~ ~ ~ ~ ~ ~