Speaker: Ezio Vasselli

Title: Nets of C^*-algebras and topological invariants

Abstract: Motivated by algebraic quantum field theory, we study nets of C^*-algebras, groups and Hilberts spaces, regarding them as analogues of bundles where the base space is replaced by a partially ordered set (poset).

In particular, we consider nets with fibre the Cuntz algebra O_d and show that the Galois correspondence between compact Lie groups and subalgebras of O_d breaks down in this more general setting.

Finally, we show that when the given poset is a subbase for the topology of a manifold, flat principal bundles and characteristic classes come naturally associated with net of C^*-algebras and their symmetric endomorphisms.

Based on joint works with J. E. Roberts and G. Ruzzi.