Some cellular subsets of the spheres

Vo Thanh Liem

Vol. 68 (1977), No. 1, 115–125

DOI: 10.2140/pjm.1977.68.115

Abstract

Let H be a PL-homology sphere such that its multisuspension S^k ∗ H is topologically homeomorphic to the sphere. We prove that every cell-like subset of S^k is cellular. Also, every non-compact PL-manifold of dimension greater than four accepts uncountably many simplicial triangulations each of which contains a non-cellular k-simplex for every k≠0.

Mathematical Subject Classification

Primary: 57C15, 57C15

Milestones

Received: 14 July 1976

Revised: 23 November 1976

Published: 1 January 1977