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On The Topological Period-Index Problem over 8-manifolds (1911.07206v1)
Published 17 Nov 2019 in math.AT and math.AG
Abstract: We establish upper bounds of the indices of topological Brauer classes over a closed orientable 8-manifolds. In particular, we verify the Topological Period-Index Conjecture (TPIC) for topological Brauer classes over closed orientable 8-manifolds of order not congruent to 2 mod 4. In addition, we provide a counter-example which shows that the TPIC fails in general for closed orientable 8-manifolds.