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.

https://bbb.mpim-bonn.mpg.de/b/gae-a7y-hhd

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