A spatial approach to Poincaré duality on singular spaces: intersection space cohomology

Timo Essig
MINT-Kolleg Baden-Württemberg, Karlsruher Institut für Technologie (KIT)

Date(s) : 09/04/2018   iCal
15 h 30 min - 16 h 30 min

Manifolds have a remarkable hidden symmetry: Poincaré Duality, which is visible in (co)homology. Particularly, the ranks of the (co)homology groups of complementary degree are equal. This property enables us to understand the topology of manifolds much better, for example by defining and investigating the signature. Singular spaces do not have that symmetry in general. To be able to use similar techniques as for manifolds, one has to replace ordinary (co)homology by an alternative. In this talk, we present an approach that was introduced by M. Banagl: Intersection space (co)homology. We discuss the spatial and the de Rham picture for spaces with isolated singularities and talk about the difficulties of generalizing the theory to pseudomanifolds with more complicated singularities.



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