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
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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