Exercise 4.4.23. Show that for \(n \geq 0\) and \(k + n \geq 0\) we have \(\pi _k(X) \cong \pi _{n+k}(X_n)\). In particular we have \(\pi _k(X) = \pi _k(\Omega ^{\infty }X)\) for \(k \geq 0\).
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Stable homotopy theory and higher algebra · Exercise 4.4.23
Exercise 4.4.23. Show that for \(n \geq 0\) and \(k + n \geq 0\) we have \(\pi _k(X) \cong \pi _{n+k}(X_n)\). In particular we have \(\pi _k(X) = \pi _k(\Omega ^{\infty }X)\) for \(k \geq 0\).
Generated from the authoritative LaTeX source.