On the period and index of topological Azumaya algebras on 8-manifolds.
I will report on joint work in progress with Diarmuid Crowley and Xing Gu regarding the relationship between the period (ie. order) of a class in the topological Brauer group and its index. I will outline a proof that for an odd-period Brauer class on a compact orientable 8-manifold, the index divides the cube of the period. This is false for generic 8-complexes as was shown by Gu. If time permits I will discuss the situation at the prime 2.
Professor Christian Haesemeyer, University of Melbourne