RECENT RESULTS ON INTERSECTION SPACE COHOMOLOGY (Research on topology and differential geometry using singularity theory of differentiable maps)

In this article, recent results on the theory of intersection spaces and their cohomology groups are reviewed. The focus is on the construction of intersection spaces for non-isolated singularities and stratification depth greater than one as well as on the de Rham, sheaf theoretic and algebraic approaches towards intersection space cohomology. At the end, a list of open problems is provided.