Abstract
By comparing the Postnikov towers of the classifying spaces of projective unitary groups and the differentials in a twisted Atiyah-Hirzebruch spectral sequence, we deduce a lower bound on the topological index in terms of the period, and solve the topological version of the period-index problem in full for finite CW complexes of dimension less than 6. Conditions are established that, if they were met in the cohomology of a smooth complex 3-fold variety, would disprove the ordinary period-index conjecture. Examples of higher-dimensional varieties meeting these conditions are provided. We use our results to furnish an obstruction to realizing a period-2 Brauer class as the class associated to a sheaf of Clifford algebras, and varieties are constructed for which the total Clifford invariant map is not surjective. No such examples were previously known.
Original language | English (US) |
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Article number | jtt042 |
Pages (from-to) | 617-640 |
Number of pages | 24 |
Journal | Journal of Topology |
Volume | 7 |
Issue number | 3 |
DOIs | |
State | Published - Sep 2014 |
ASJC Scopus subject areas
- Geometry and Topology