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The Topological Period-Index Problem over 8-Complexes, II · Around

2018

The Topological Period-Index Problem over 8-Complexes, II

Gu, Xing

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We complete the study of the topological period-index problem over 8 dimensional finite CW complexes started in a preceding paper.

More precisely, we determine the sharp upper bound of the index of a topological Brauer class $\alpha\in H^3(X;\mathbb{Z})$, where $X$ is of the homotopy type of an 8 dimensional finite CW complex and the period of $\alpha$ is divisible by 4.

Built on

Séminaire Henri Cartan: ann. 7 1954/1955; Algèbres d’Eilenberg-Maclane et homotopie
É. normale supérieure (France) and H. Cartan · 1958
Earlier work this paper cites.
Le groupe de Brauer. I. algebres d’Azumaya et interprétations diverses
A. Grothendieck · 1968
Earlier work this paper cites.
A user’s guide to spectral sequences
J. McCleary · 2001
Earlier work this paper cites.
Exposant et indice d’algèbres simples centrales non ramifiées
J.-L. Colliot-Thélene · 2002
Earlier work this paper cites.

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Then

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