Higher homotopy associativity in the Harris decomposition of Lie groups

For certain pairs of Lie groups (G, H) and primes p, Harris showed a relation of the p-localized homotopy groups of G and H. This is reinterpreted as a p-local homotopy equivalence G ≃ (p)H × G/H, and so there is a projection G(p) → H(p). We show how much this projection preserves the higher homotop...

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Bibliographic Details
Published inProceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 150; no. 6; pp. 2982 - 3000
Main Authors Kishimoto, Daisuke, Miyauchi, Toshiyuki
Format Journal Article
LanguageEnglish
Published Edinburgh, UK Royal Society of Edinburgh Scotland Foundation 01.12.2020
Cambridge University Press
Subjects
Associativity
Lie groups
55Q15
mod p decomposition
55P35
Lie group
higher homotopy associativity
higher homotopy commutativity
55P60
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Summary:For certain pairs of Lie groups (G, H) and primes p, Harris showed a relation of the p-localized homotopy groups of G and H. This is reinterpreted as a p-local homotopy equivalence G ≃ (p)H × G/H, and so there is a projection G(p) → H(p). We show how much this projection preserves the higher homotopy associativity.
ISSN:0308-2105
1473-7124
DOI:10.1017/prm.2019.57