GATP-Seminar – Geordie Williamson (Sydney)

Wird ins Deutsche übersetzt…

Intersection (co)homology is a beautiful invariant of singular spaces, e.g. singular complex algebraic varieties. Over the rationals it satisfies a raft of strong properties (e.g. Poincaré duality, hard Lefschetz, pure Hodge structure,…) which still seem like a miracle. In their paper introducing these groups, Goresky and MacPherson point out that (unlike the integral cohomology of smooth manifolds) it fails to satisfy Poincaré duality over the integers. Subsequent sheaf theoretic approaches have clarified the situation, and in fact one can prove that there is no reasonable theory over the in…