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Bounding size of homotopy groups of spheres

Bounding size of homotopy groups of spheres
Bounding size of homotopy groups of spheres
Let p be prime. We prove that, for n odd, the p-torsion part of πq(Sn) has cardinality at most and hence has rank at most 21/(p−1)(q−n+3−2p). for p = 2, these results also hold for n even. The best bounds proven in the existing literature are and 2q−n+1, respectively, both due to Hans–Werner Henn. The main point of our result is therefore that the bound grows more slowly for larger primes. As a corollary of work of Henn, we obtain a similar result for the homotopy groups of a broader class of spaces.
0013-0915
1100-1105
Boyde, Guy
5c470bc9-cf8d-4481-9674-db1ea2bf7293
Boyde, Guy
5c470bc9-cf8d-4481-9674-db1ea2bf7293

Boyde, Guy (2020) Bounding size of homotopy groups of spheres. Proceedings of the Edinburgh Mathematical Society, 63 (4), 1100-1105. (doi:10.1017/S001309152000036X).

Record type: Article

Abstract

Let p be prime. We prove that, for n odd, the p-torsion part of πq(Sn) has cardinality at most and hence has rank at most 21/(p−1)(q−n+3−2p). for p = 2, these results also hold for n even. The best bounds proven in the existing literature are and 2q−n+1, respectively, both due to Hans–Werner Henn. The main point of our result is therefore that the bound grows more slowly for larger primes. As a corollary of work of Henn, we obtain a similar result for the homotopy groups of a broader class of spaces.

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More information

Accepted/In Press date: 12 October 2020
Published date: 5 November 2020
Additional Information: Copyright © The Author(s), 2020. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

Identifiers

Local EPrints ID: 457722
URI: http://eprints.soton.ac.uk/id/eprint/457722
ISSN: 0013-0915
PURE UUID: d21bcf4f-3066-454b-b718-a72a0d01ba7f

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Date deposited: 16 Jun 2022 00:24
Last modified: 16 Jun 2022 00:24

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Author: Guy Boyde

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