Other forms of duality

30 maio 2019, 10:30 • Gustavo Granja

Remarks on the H_{n-1} and H^n of a manifold following from the computation of the top homology. Compactly supported cohomology of a locally compact space. Functoriality with respect to proper maps and open embeddings. Examples. The system of fundamental classes for an arbitrary oriented manifold and statement of Poincaré duality for such. Sketch proof. Manifolds with boundary. Existence of collarings. Orientations. Statement of Lefschetz duality. Cech cohomology and Alexander duality for the homology of a complement of a compact set in a sphere. Example: RP^2 does not embed in R^3.