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p-Hyperbolicity of homotopy groups via K-theory

p-Hyperbolicity of homotopy groups via K-theory
p-Hyperbolicity of homotopy groups via K-theory

We show that Sn∨ Sm is Z/ pr-hyperbolic for all primes p and all r∈ Z+, provided n, m≥ 2 , and consequently that various spaces containing Sn∨ Sm as a p-local retract are Z/ pr-hyperbolic. We then give a K-theory criterion for a suspension Σ X to be p-hyperbolic, and use it to deduce that the suspension of a complex Grassmannian Σ Grk,n is p-hyperbolic for all odd primes p when n≥ 3 and 0 < k< n. We obtain similar results for some related spaces.

K-theory, Local hyperbolicity
0025-5874
Boyde, Guy
5c470bc9-cf8d-4481-9674-db1ea2bf7293
Boyde, Guy
5c470bc9-cf8d-4481-9674-db1ea2bf7293

Boyde, Guy (2021) p-Hyperbolicity of homotopy groups via K-theory. Mathematische Zeitschrift. (doi:10.1007/s00209-021-02917-1).

Record type: Article

Abstract

We show that Sn∨ Sm is Z/ pr-hyperbolic for all primes p and all r∈ Z+, provided n, m≥ 2 , and consequently that various spaces containing Sn∨ Sm as a p-local retract are Z/ pr-hyperbolic. We then give a K-theory criterion for a suspension Σ X to be p-hyperbolic, and use it to deduce that the suspension of a complex Grassmannian Σ Grk,n is p-hyperbolic for all odd primes p when n≥ 3 and 0 < k< n. We obtain similar results for some related spaces.

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Accepted/In Press date: 27 September 2021
e-pub ahead of print date: 30 September 2021
Additional Information: Publisher Copyright: © 2022, The Author(s). Copyright: Copyright 2022 Elsevier B.V., All rights reserved.
Keywords: K-theory, Local hyperbolicity

Identifiers

Local EPrints ID: 454491
URI: http://eprints.soton.ac.uk/id/eprint/454491
ISSN: 0025-5874
PURE UUID: 64a84c9e-d5db-46c7-82a2-dc6fa1317fee

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Date deposited: 11 Feb 2022 17:34
Last modified: 05 Jun 2024 18:58

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Author: Guy Boyde

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