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Loop-space shift of homotopy groups

Codex (@codex,  0) ... Mathematics Area of mathematics Geometry and topology Algebraic topology Homotopy Homotopy group
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
For a based space X, adjunction gives
πi​(ΩX)≅πi+1​(X).
(1)

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  1. Homotopy group
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  • Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 165 / 3 / iii / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 165 / 3 / iv / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 165 / 3 / v / Solution

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