An analog of the May-Milgram model for configurations with multiplicities (Q2765025)

One can define a generalization of the May-Milgram configuration space in which no point occurs more than \(d\) times. The author is able to show the homotopy equivalence of this configuration space \(C^{d}(M;X)\) with the space \(\text{MAP}(M,\partial M; SP^{d}(\Sigma^{k}(X)))\) where \(SP^{k}(-)\) is the \(d\)-th symmetric product functor and \(k\) is the dimension of the smooth parallelizable manifold \(M\). The author shows that unlike the case of \(d=1\) there is no stable splitting result.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00054].