Simply-connected manifolds with large homotopy stable classes

Conway, Anthony; Crowley, Diarmuid; Powell, Mark; Sixt, Joerg

Abstract

For every k ≥ 2 and n ≥ 2 we construct n pairwise homotopically inequivalent simply-connected, closed 4k-dimensional manifolds, all of which are stably diffeomorphic to one another. Each of these manifolds has hyperbolic intersection form and is stably parallelisable. In dimension 4, we exhibit an analogous phenomenon for spinc structures on S2 × S2. For m ≥ 1, we also provide similar (4m−1)-connected 8m-dimensional examples, where the number of homotopy types in a stable diffeomorphism class is related to the order of the image of the stable J-homomorphism π4m−1(SO) → πs 4m−1.

Citation

Conway, A., Crowley, D., Powell, M., & Sixt, J. (2023). Simply-connected manifolds with large homotopy stable classes. Journal of the Australian Mathematical Society, 115(2), 172-203. https://doi.org/10.1017/s1446788722000167

• Journal Article Type: Article
• Acceptance Date: Jun 26, 2022
• Online Publication Date: Sep 26, 2022
• Publication Date: 2023-10
• Deposit Date: Aug 12, 2022
• Publicly Available Date: Oct 25, 2022
• Journal: Journal of the Australian Mathematical Society
• Print ISSN: 1446-7887
• Electronic ISSN: 1446-8107
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 115
• Issue: 2
• Pages: 172-203
• DOI: https://doi.org/10.1017/s1446788722000167
• Public URL: https://durham-repository.worktribe.com/output/1194534
• Related Public URLs: https://arxiv.org/abs/2109.00654