The period-index problem for twisted topological K-theory

@article{Antieau2014ThePP,
  title={The period-index problem for twisted topological K-theory},
  author={Benjamin Antieau and Ben Williams},
  journal={Geometry \& Topology},
  year={2014},
  volume={18},
  pages={1115-1148}
}
We introduce and solve a period-index problem for the Brauer group of a topological space. The period-index problem is to relate the order of a class in the Brauer group to the degrees of Azumaya algebras representing it. For any space of dimension d, we give upper bounds on the index depending only on d and the order of the class. By the Oka principle, this also solves the period-index problem for the analytic Brauer group of any Stein space that has the homotopy type of a finite CW-complex… 
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