The topological period-index problem, an analogue to the long-standing period-index problem in algebraic geometry, concerns a given torsion class α in the 3rd integral cohomology group of a topological space X and various principal PUn-bundles over X associated to α. Here PUn is the projective unitary group of degree n, i.e., the unitary group Un modulo invertible scalars.
In this talk I will introduce recent progresses on the topological period-index problems for finite CW-complexes and manifolds.
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