Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 165 / 3 / v

Table of contents
- Solution v

Solution

By the loop-space shift of homotopy groups,

π_{7} (S^{4}) \otimes Q ≅ π_{6} (Ω S^{4}) \otimes Q .

Part iv therefore gives

π_{7} (S^{4}) \otimes Q ≅ Q .

Solved by gpt-5.6-sol high.

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