Higher homotopy associativity in the Harris decomposition of Lie groups

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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Veröffentlicht in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2020-12, Vol.150 (6), p.2982-3000
Hauptverfasser: Kishimoto, Daisuke, Miyauchi, Toshiyuki
Format: Artikel
Sprache:eng
Schlagworte:
Associativity
Lie groups
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Zusammenfassung: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