Configuration spaces on punctured manifolds
type: Item
instance of: scholarly article
title: Configuration spaces on punctured manifolds
zbMATH Open document ID: 1010.55011
DOI: 10.12775/TMNA.2002.023
author: Edward Fadell
author: S. Y. Husseini
published in: Topological Methods in Nonlinear Analysis
publication date: 2003-03-09T00:00:00Z
review text: Among others, the authors study homotopy properties of the fibration \[ {\mathbf F}_{k-r}(M_{r+1})\to{\mathbf F}_{k}(M_1)\to{\mathbf F}_r(M_1), \] where \(M\) is a (smooth) simply connected \(n+1 > 2\) manifold, and \({\mathbf F}_i(M_j)\) is the space of configurations of \(i\) points in \(M\) with \(j\) points removed. For example, in particular they find that a necessary condition for this fibration to be fiber homotopically trivial is that \(n=3\) or 7 and \(r=2\). Study of the Lie algebras, \(\pi_*({\mathbf F}_{k+1}(M_i))\), \(i=0,1\), is part of the investigation.
Mathematics Subject Classification ID: 55R80
Mathematics Subject Classification ID: 55R05
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 1869652
zbMATH Keywords: configuration space
zbMATH Keywords: manifold
zbMATH Keywords: homotopy
zbMATH Keywords: Lie algebra
zbMATH Keywords: fiber space
reviewed by: Lee P. Neuwirth
MaRDI profile type: Publication
full work available at URL: tmna.2002.023
OpenAlex ID: W2547868065
description: scientific article; zbMATH DE number 1869652