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Explore a lecture by John Morgan from Columbia University on Poincare/Lefschetz Duality Bordism Theory. Learn about studying cohomology theories through cycles with numerical invariants, examining how classes in cohomology theory are determined by their invariants on cycles mapping to a space. Discover several examples of this paradigm, including ordinary cohomology with pseudo-manifolds and complex K-theory with almost complex bordism quotients. The lecture primarily focuses on using Intersection cohomology to construct a bordism theory that serves as a dual to the basic cohomology theory of surgery. This one-hour presentation from IMSA delves into the mathematical foundations of duality in bordism theory and its applications to cohomology.
