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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The structure of the spin$^h$ bordism spectrum
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by Keith Mills;
Proc. Amer. Math. Soc. 152 (2024), 3605-3616
DOI: https://doi.org/10.1090/proc/16748
Published electronically: June 12, 2024

Abstract:

Spin$^h$ manifolds are the quaternionic analogue to $\text {spin}^c$ manifolds. We compute the $\text {spin}^h$ bordism groups at the prime $2$ by proving a structure theorem for the cohomology of the $\text {spin}^h$ bordism spectrum $\mathrm {MSpin^h}$ as a module over the mod 2 Steenrod algebra. This provides a 2-local splitting of $\mathrm {MSpin^h}$ as a wedge sum of familiar spectra. We also compute the decomposition of $H^*(\mathrm {MSpin^h};\mathbb {Z}/2\mathbb {Z})$ explicitly in degrees up through 30 via a counting process.
References
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Bibliographic Information
  • Keith Mills
  • Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
  • ORCID: 0000-0001-6376-0128
  • Email: kmills96@umd.edu
  • Received by editor(s): July 18, 2023
  • Received by editor(s) in revised form: November 16, 2023, November 20, 2023, and December 8, 2023
  • Published electronically: June 12, 2024
  • Communicated by: Julie Bergner
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 3605-3616
  • MSC (2020): Primary 55N22; Secondary 55T15, 55S10
  • DOI: https://doi.org/10.1090/proc/16748
  • MathSciNet review: 4767288