Mathematical Physics Seminar, July 20, 2010
K-homology, the dual of K-theory, is the generalized homology theory of (abstract) elliptic operators over (not necessarily commutative) spaces. Important operators in differential geometry determine elements in K-homology which can then be used to study those spaces using the methods of algebraic topology (notable applications include Kasparov's work on the Novikov conjecture). In my talk, I will introduce Kasparov's original analytic description as well as a geometric picture due to Baum and Douglas, inspired by singular bordism, and sketch why both theories are equivalent. |