### Topological K-theory of C*-algebras for the Working Mathematician – Lecture 4 (K-homology and Brown-Douglas-Fillmore)

My notes of Haim’s Schochet’s fourth lecture in this series is here below.

It is impossible to start without mention that Alexander Grothendieck passed away last week. Grothendieck is considered by many as one of the greatest mathematicians of 20th century, and his contributions affect the material in this lecture series in at least two significant ways. As we mentioned, a first version of K-theory was developed by Grothendieck opening the door for topological K-theory (which, in turn, opened the door for K-theory of C*-algebras). Grothendieck also developed the theory of nuclear topological vector spaces and tensor products of topological vector spaces, a theory that has influenced the development of the concepts of nuclearity and tensor product which are central to contemporary C*-algebra theory. Read the rest of this entry »