Collapses, products and LC manifolds
arXiv:0911.4656 · doi:10.1016/j.jcta.2010.05.001
Abstract
Durhuus and Jonsson (1995) introduced the class of "locally constructible" (LC) triangulated manifolds and showed that all the LC 2- and 3-manifolds are spheres. We show here that for each d>3 some LC d-manifolds are not spheres. We prove this result by studying how to collapse products of manifolds with exactly one facet removed.
6 pages; added references; minor changes. Accepted for J. Comb. Theory, Series A