ON STABLE HOMOTOPY EQUIVALENCES
Copyright policy )ON STABLE HOMOTOPY EQUIVALENCES
Let \(QX = \varinjlim \Omega^n \Sigma^nX\) be the free infinite loop space generated by the space \(X\). Let \(X\) and \(Y\) be finite CW complexes. The authors prove that if \(QX\) and \(QY\) are homotopy equivalent, then for some large integer \(n\), \(\Sigma^nX\) and \(\Sigma^n Y\) are homotopy equivalent. The authors rely on the genus cancellation techniques found in \textit{C. Wilkerson}'s ``Genus and cancellation'' [Topology 14, 29-36 (1975; Zbl 0315.55016)]. The paper ends with examples and conjectures concerning the possible unique delooping of \(QX\).
- University of Rochester United States
stable homotopy, delooping, Stable homotopy theory, spectra, genus cancellation, Homotopy equivalences in algebraic topology, free infinite loop space
stable homotopy, delooping, Stable homotopy theory, spectra, genus cancellation, Homotopy equivalences in algebraic topology, free infinite loop space
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