Physical Sciences and Mathematics Commons^™

The Poincaré Duality Theorem And Its Applications, Natanael Alpay, Melissa Sugimoto, Mihaela Vajiac

SURF Posters and Papers

In this talk I will explain the duality between the deRham cohomology of a manifold M and the compactly supported cohomology on the same space. This phenomenon is entitled “Poincaré duality” and it describes a general occurrence in differential topology, a duality between spaces of closed, exact differentiable forms on a manifold and their compactly supported counterparts. In order to define and prove this duality I will start with the simple definition of the dual space of a vector space, with the definition of a positive definite inner product on a vector space, then define the concept of a manifold. …