Compact contractible \(n\)-manifolds have arc spines \((n\geq 5)\)
type: Item
instance of: scholarly article
title: Compact contractible \(n\)-manifolds have arc spines \((n\geq 5)\)
zbMATH Open document ID: 0820.57014
author: Fredric D. Ancel
author: Craig R. Guilbault
published in: Pacific Journal of Mathematics
publication date: 1995-08-22T00:00:00Z
review text: The following two theorems were motivated by questions about the existence of disjoint spines in compact contractible manifolds. Theorem 1. Every compact contractible \(n\)-manifold \((n\geq 5)\) is the union of two \(n\)-balls along a contractible \((n-1)\)-dimensional submanifold of their boundaries. A compactum \(X\) is a spine of a compact manifold \(M\) if \(M\) is homeomorphic to the mapping cylinder of a map from \(\partial M\) to \(X\). Theorem 2. Every compact contractible \(n\)-manifold \((n\geq 5)\) has a wild arc spine. Also a new proof is given that for \(n\geq 6\), every homology \((n-1)\)- sphere bounds a compact contractible \(n\)-manifold. The implications of arc spines for compact contractible manifolds of dimensions 3 and 4 are discussed in section 5. The questions about the existence of disjoint spines in compact contractible manifolds which motivated the preceding theorems are stated in section 6.
Mathematics Subject Classification ID: 57N15
zbMATH DE Number: 779060
zbMATH Keywords: compact contractible manifolds
zbMATH Keywords: wild arc spine
MaRDI profile type: Publication
full work available at URL: pjm.1995.168.1
OpenAlex ID: W2028956889
DOI: 10.2140/PJM.1995.168.1
description: scientific article; zbMATH DE number 779060