Mapping Cylinders and Manifolds
Hiroshi Ikeda, Masakatsu Yamashita · Institutional Repositories DataBase (IRDB) · 1979
IntroductionLet P and Q be polyhedra.For a map f from P to Q, we denote the mapping cylinder of f by Cf, that is,where I means the closed unit interval (0, l] and + means the disjoint union.The standard simplicial structure of Cf is explained later. 0Let W be a manifold and P a subpolyhedron in the interior W of W.By N(P, W), we denote the regular neighborhood of P in W. It.is well-known that there exists a map f from N(P, W) to P satisfying (N(P, W), P) = (Cf' P), where N(P, W) means the boundary of N(P, W) (see for examp e [l]).In this paper, we are interested in the following problem.Problem.Let W and P be a manifold and a polyhedron, respectively, and let f be a map from W to P. Find a necessary and sufficient con- dition on f for Cf to be a manifold.In [l], M. Cohen obtained the following results.