Glueing of closed points and algebraic and topological fundamental group (Q793105)

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.