Homology \(n\)-spheres as codimension-\((n+1)\) shape m\(_{\text{simpl}}\)-fibrators
Let \(N\) be a closed, orientable, PL \(n\)-manifold such that every \(f:N\to N\) inducing a \(\pi_1\)-isomorphism is a homotopy equivalence; every epimorphism \(\pi_1(N)\to\pi_1(N)\) is an isomorphism; \(H_i(N)=0\) for \(0<i<k-1\leq n\) for some \(k>2\). Then \(N\) is a codimension-\(k\) shape m\(_{\text{simpl}}\)-fibrator, i.e. every \(N\)-shaped PL map \(p:M\to B\), \(M\) a closed PL \((n+k)\)-manifold and \(B\) a simplicial triangulated \(k\)-manifold, is an approximate fibration.
manifold homotopically determined by \(\pi_1\)
scientific article; zbMATH DE number 5290944
scientific article