The realizability of local loop spaces as manifolds
The main results of this paper are: Let \(P\) be a collection of primes and \(X\) a \(P\)-local \(\mathbb Z_{(P)}\)-finite loop space. Then \(X\) is homotopy equivalent to the \(P\)-localization of a compact, smooth, parallelizable manifold and an analogous result holds in the \(P\)-complete case (under a more technical hypothesis). A consequence is that every \(p\)-compact group is the \(p\)-completion of a compact, smooth, and parallelizable manifold.
scientific article; zbMATH DE number 5125380