Algebraic topology for $C^*$-algebras II. Covering spaces, cobordism, Chern character, and Connes quantization

By Gelfand's theorem, a commutative $C^*$-algebra is completely determined by its spectrum. We consider the Gelfand space, which is more informative than the spectrum. The Gelfand space coincides with the spectrum in the commutative case, and in many cases it completely determines the respective noncommutative $C^*$-algebra.
Also, the Gelfand space yields $C^*$-algebraic generalizations for a number of notions of algebraic topology. This was the subject of our earlier talk. The present talk is a continuation of the previous one, and it involves generalizations of the following notions:
- covering spaces;
- cobordism;
- the Chern character.
We also develop Connes quantization theory on the basis of Alain Connes' factorization construction.