Two completion towers for generalized homology (Q2707507)

The purpose of this paper is to construct two completion towers of approximation for a generalized homology theory. The construction uses only principal fibrations and is done by successively correcting the homology of the partial tower given inductively.NEWLINENEWLINENEWLINEThe author presents some properties of the two completion towers, e.g. pro-idempotency, preservation of generalized homology and a Dwyer result. It is also shown (Theorem 1.1) that ``for \(X\) a \(2\)-\(U\)-polyGEM (where \(U\) is the spectrum associated to the multiplicative generalized homology \(h_*\)), the \(E_\infty\)-term of the unstable Adams spectral sequence associated to \(h_*\) contains, as a retract, the desired homotopy group of \(X\)''.NEWLINENEWLINEFor the entire collection see [Zbl 0955.00041].