Obstructions to embedding disks. II: A proof of a conjecture of Hudson
type: Item
instance of: scholarly article
title: Obstructions to embedding disks. II: A proof of a conjecture of Hudson
zbMATH Open document ID: 0547.57014
DOI: 10.1016/0166-8641(84)90036-1
author: Nathan Habegger
published in: Topology and its Applications
publication date: 1984-01-01T00:00:00Z
review text: This paper is concerned with the problem of representing an element of \(\pi_ n(W,\partial W)\) by a properly imbedded disk - W is a PL-manifold of dimension m. J. F. P. Husdon defines an obstruction in \(H_{2n- m+1}(W,\partial W;G)\) where \(G={\mathbb{Z}}\) or \({\mathbb{Z}}/2\) as m-n is odd or even. In certain cases Hudson proves that the vanishing of this obstruction is sufficient for the existence of an imbedding. For example, \(m\geq n+3\) and (W,\(\partial W) (2n-m)-\)connected are certainly necessary conditions, but Hudson also requires m-n even and \(\pi_ 1(W)=\pi_ 1(\partial W)=0.\) In the present paper these latter conditions are eliminated and the obstructions are generalized to encompass the problem of representing several elements of \(\pi_ n(W,\partial W)\) by disjointly imbedded disks. In carrying out this project intersection and self-intersection invariants are introduced in the homology of \((\tilde W,\partial\tilde W)\), the universal covering pair of (W,\(\partial W)\).
Mathematics Subject Classification ID: 57Q35
Mathematics Subject Classification ID: 57R95
Mathematics Subject Classification ID: 57R40
zbMATH DE Number: 3872292
zbMATH Keywords: intersection invariants
zbMATH Keywords: representation of elements in relative homotopy groups
zbMATH Keywords: imbedded disk
zbMATH Keywords: PL-manifold
zbMATH Keywords: self-intersection invariants
zbMATH Keywords: homology
zbMATH Keywords: universal covering pair
Wikidata QID: Q122875915
reviewed by: Jerome Levine
MaRDI profile type: Publication
full work available at URL: 0166-8641(84)90036-1
OpenAlex ID: W2014150916
cites work: Enlacements de sphères en co-dimension supérieure à 2
cites work: Q4766257
cites work: Q5584509
cites work: Piecewise linear embeddings
cites work: Classification problems in differential topology. IV: Thickenings
cites work: Unknotting combinatorial balls
cites work: Embedding up to homotopy type - the first obstruction
description: scientific article; zbMATH DE number 3872292