Glueing of closed points and algebraic and topological fundamental group
type: Item
instance of: scholarly article
title: Glueing of closed points and algebraic and topological fundamental group
zbMATH Open document ID: 0538.14011
author: Angelo Vistoli
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1983-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/107897
review text: Let X and Y be topological spaces such that Y is obtained from X by glueing \(p+1\) distinct points of X. The author shows that \(\pi_ 1(Y)\simeq \pi_ 1(X)*L_ p,\) where * denotes the free product and \(L_ p\) is the free group on p generators. - Moreover, if X and Y are algebraic varieties, the author shows that \(\pi_ 1^{alg}(Y)\simeq(\pi_ 1^{alg}(X)*L_ p)^ 1,\) where 1 denotes the completion with respect to a topology which can be canonically defined.
Mathematics Subject Classification ID: 14F35
Mathematics Subject Classification ID: 14E20
Mathematics Subject Classification ID: 55Q05
Mathematics Subject Classification ID: 14F45
zbMATH DE Number: 3855269
zbMATH Keywords: algebraic fundamental group
zbMATH Keywords: topological fundamental group
MaRDI profile type: Publication
cites work: Q5622916
cites work: Q4200313
cites work: Incollamenti di ideali primi e gruppi di Picard
cites work: Q5522742
cites work: Q5605674
description: scientific article; zbMATH DE number 3855269