The homotopy groups of the homotopy fibre of an induced map of function spaces (Q2734863)

Let \(u: X\to Y\) and \(g: Y\to B\) be maps between topological spaces. The authors construct a long exact sequence of groups and pointed sets in which the groups are the track groups \(\pi_n^X(Y;u)\) and \(\pi_n^X(B;gu)\) together with some new groups \(\pi_{n-1}(X,Y/B)\). The new groups are isomorphic to homotopy groups of the homotopy fibre of \(g\), and are obtained by interpreting \(n\)-tracks as \(2\)-morphisms in homotopy \(2\)-groupoids. The authors also construct a secondary operation and describe an application to spaces of homotopy equivalences.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00050].