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
Boyde, Guy
5c470bc9-cf8d-4481-9674-db1ea2bf7293
Boyde, Guy
5c470bc9-cf8d-4481-9674-db1ea2bf7293
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.
Text
Boyde2022_Article_P-HyPerbolicityOfHomotoPyGrouP
- Version of Record
More information
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
Catalogue record
Date deposited: 11 Feb 2022 17:34
Last modified: 16 Mar 2024 15:35
Export record
Altmetrics
Contributors
Author:
Guy Boyde
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics