Single Loop Space Decompositions
Copyright policy )Single Loop Space Decompositions
The method of single loop space decompositions, in which Ω X \Omega X is factored into minimal factors, is an important one for understanding the unstable homotopy of many simply-connected spaces X X . This paper begins with a survey of the major known theorems along these lines. We then give a necessary and sufficient condition for Ω X \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.
product decompositions of loop spaces of finite complexes, Homotopy groups of wedges, joins, and simple spaces, \(H\)-spaces and duals, Moore spaces, Bockstein spectral sequence, \(p\)-local atomic \(H\)-spaces, Loop spaces
product decompositions of loop spaces of finite complexes, Homotopy groups of wedges, joins, and simple spaces, \(H\)-spaces and duals, Moore spaces, Bockstein spectral sequence, \(p\)-local atomic \(H\)-spaces, Loop spaces
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