Disjoint spine phenomena in certain contractible n-manifolds (n⩾5)

Abstract

If M is a compact PL manifold with boundary containing a subpolyhedron K in its interior, then K is said to be a PL spine of M provided M collapses to K (M↘K). Guilbault [Topology 34 (1) (1995) 99–108] has shown that certain nontrivial contractible manifolds possess disjoint spines. His results stem from a standing conjecture regarding disjoint spines in contractible 4-manifolds constructed by Mazur. More to the point, there is a dimensional requirement introduced by his techniques; Guilbault produces such manifolds in dimensions n⩾9. We shall provide techniques which allow the construction of examples in dimensions n⩾5 following the path laid out by Guilbault. The new techniques will provide a slight strengthening of some other Guilbault results as well.