The topological period-index problem over $8$-complexes, II
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Abstract:
We complete the study of the topological period-index problem over $8$-dimensional connected 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 $4$.References
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Additional Information
- Xing Gu
- Affiliation: Max Plank Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany; and School of Mathematics and Statistics, the University of Melbourne, Parkville VIC 3010, Australia
- ORCID: 0000-0003-0866-8403
- Email: gux2006@mpim-bonn.mpg.de
- Received by editor(s): June 4, 2019
- Received by editor(s) in revised form: March 3, 2020
- Published electronically: July 20, 2020
- Additional Notes: The bulk of this work was completed at the University of Melbourne, Australia, and further revisions were made at the Max Planck Institute for Mathematics, Germany. The author is grateful to the Australian Research Council, the University of Melbourne and the Max Planck Institute for Mathematics for their support.
- Communicated by: Mark Behrens
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 4531-4545
- MSC (2010): Primary 55S45; Secondary 55R20
- DOI: https://doi.org/10.1090/proc/15112
- MathSciNet review: 4135317