Published on *Max Planck Institute for Mathematics* (https://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Xing Gu
Affiliation:

University of Melbourne/MPIM
Date:

Tue, 2020-03-31 14:00 - 15:00 The topological period-index problem (TPIP), an analogue to the long-standing period-index conjecture in algebraic geometry, concerns a given torsion class α in the 3rd integral cohomology group of a topological space X and various principal PU_n-bundles over X associated to α. Here PU_n is the projective unitary group of order n, i.e., the unitary group U_n modulo invertible scalars. TPIP was first considered by Antieau and Williams in an attempt to find a counterexample to the period-index conjecture, but later turned out to have its own significance.

In this talk I will introduce recent work, joint with Crowley and Haesemeyer on the topological period-index problems over finite CW-complexes and manifolds.

**Links:**

[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] https://www.mpim-bonn.mpg.de/node/3444

[3] https://www.mpim-bonn.mpg.de/node/5312