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Transactions of the American Mathematical Society

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Single loop space decompositions

Author: David J. Anick
Journal: Trans. Amer. Math. Soc. 334 (1992), 929-940
MSC: Primary 55P35; Secondary 55Q20
MathSciNet review: 1145728
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Abstract: The method of single loop space decompositions, in which $ \Omega X$ is factored into minimal factors, is an important one for understanding the unstable homotopy of many simply-connected spaces $ X$. This paper begins with a survey of the major known theorems along these lines. We then give a necessary and sufficient condition for $ \Omega X$ to be decomposable as a product of spaces belonging to a certain list. We conclude with a nontrivial instance of an application of this condition.

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