2:00 pm Wednesday, November 2, 2005
Junior Topology Seminar: Poincare Duality by Joao Nogueira in RLM 11.176
In this talk I will present a modern proof by Milnor of the Poincare duality theorem. The assertion was first used by Poincare in 1893, as if it were completely obvious, to prove that the Euler-Poincare characteristic of a compact manifold of odd dimension is 0. However it took approximately 40 years, until the appearance of co-homology theory in the mid 30s, for Poincare duality to get completely understood and solved. In its modern version, it states that the co-homology group of a orientable n-manifold H^q(M) (like Cech co-homology, co-homology with compact support or singular co-homology) is isomorphic to the homology group of complementary degree H_{n-q}(M). I will try to make it understandable for everyone who knows the definition of homology theory and orientation of a manifold. Submitted by
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