Braid groups in complex Grassmannians
type: Item
instance of: scholarly article
title: Braid groups in complex Grassmannians
zbMATH Open document ID: 1361.57002
author: Sandro Manfredini
author: Simona Settepanella
published in: Topology and its Applications
publication date: 2014-08-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/1311.5643
review text: The authors study the ordered configuration spaces \(\mathcal F_h(k,n)\) of \(h\) distinct points in the Grassmannian \(\mathrm{Gr}(k,n)\) of \(k\)-planes in complex \(n\)-space. The subspace \(\mathcal F_h^i(k,n)\) comprises those \(h\)-tuples of points in \(\mathrm{Gr}(k,n)\) which generate a subspace of dimension \(i\). The first main result of the paper under review states that the spaces \(\mathcal F_h^i(k,n)\) are simply connected or empty. As a consequence the unordered version of such a space has as its fundamental group the symmetric group which permutes the \(h\) points. The second main result describes some second homotopy groups subject to conditions on \(i\), \(h\), \(k\) and \(n\).
reviewed by: Michael Joswig
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 20F36
Mathematics Subject Classification ID: 52C35
Mathematics Subject Classification ID: 55R80
zbMATH DE Number: 6334515
zbMATH Keywords: configuration spaces
zbMATH Keywords: braid groups
MaRDI profile type: Publication
OpenAlex ID: W2045093247
arXiv ID: 1311.5643
cites work: Braid groups in complex projective spaces
cites work: Braid groups in complex spaces.
cites work: On the configuration spaces of Grassmannian manifolds
cites work: Q5825483
DOI: 10.1016/J.TOPOL.2014.07.010
description: scientific article; zbMATH DE number 6334515