On thick diagonals and their complements
The author studies configuration spaces. More precisely, let \(X\) be a connected CW-complex, denote by \(D_{d}(X,n)\) the subspace of \(n\)-tuples, \((x_{1},\ldots,x_{n})\), \(x_{i}\in X\), having \(d\) coordinates which coincide and set \(F^{d+1}(X,n)=X^n\backslash D_{d}(X,n)\). In the case \(n<2d\), the author proves the existence of a splitting of the suspension, \(\Sigma D_{d}(X,n)\), in a wedge of smash products of \(X\). The example of \(D_{2}(S^m,4)\) shows the necessity of the restriction \(n<2k\). The author determines also the Euler characteristic and the cohomology ring of \(F^{n-1}(X,n)\) when \(X\) is an orientable closed manifold.
scientific article; zbMATH DE number 6483842
scientific article