The Seifert - Van Kampen theorem for the group of global sections

Authors : Sabahattin BALCI

Pages : 0-0

Doi:10.1501/Commua1_0000000453

View : 11 | Download : 7

Publication Date : 1995-01-01

Article Type : Research Paper

Abstract :Let X be the union of the subspaces Ut and U that are both öpen, patlı connected, UI2 = Uj A U2 f=. 0 and U19 is also path connected. in this paper, We first contruct the sheaf H of the fundanıental groups of a path connected space and give the characteristic fea- tures of H. Then, the homomorphisms and global sections of the sheaf H are explored. Finally it is proved that if the groups of global sections 1insert ignore into journalissuearticles values(U12, H I2); — , r insert ignore into journalissuearticles values( ü p Hj); = < S ^ R ^ and rinsert ignore into journalissuearticles values(U 2, H2); = < S2; R2 > are given, then the group Finsert ignore into journalissuearticles values(X, H); is isonıorphic to the group defined by the generators S, U and the relations R, R2 insert ignore into journalissuearticles values(J Rs . As a result of this, the sheaf H, especially the fundamental group insert ignore into journalissuearticles values(X, x); was easily calculated for any x G X.
Keywords : Seifert Van Kampen, global, sections