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higher homotopy commutativity

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Higher homotopy associativity in the Harris decomposition of Lie groups
Part of
- Homotopy groups
- Homotopy theory
Daisuke Kishimoto, Toshiyuki Miyauchi
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 6 / December 2020

Published online by Cambridge University Press:

11 September 2019, pp. 2982-3000

Print publication:

December 2020
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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.