分野別セミナー

Banagl's theory of intersection spaces assigns cell complexes to certain stratified topological pseudomanifolds depending on a perversity function in the sense of intersection homology. The main property of the intersection spaces is Poincar\'e duality over complementary perversities for the reduced singular (co)homology groups with rational coefficients (HI). This (co)homology theory is not isomorphic to intersection homology (IH), instead both are related by mirror symmetry.

There is also a de Rham description for the intersection space cohomology theory (HI) on certain pseudomanifolds satisfying a flatness condition for the link bundles of the singular strata.

In this talk, we give an overview of the theory, focusing on the definition and comparison of the different approaches and some easy examples.