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

Year 1995, Volume: 44 , 0 - 0, 01.01.1995

Sabahattin Balcı

https://doi.org/10.1501/Commua1_0000000453

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 1(U12, H I2) — , r ( ü p Hj) = < S ^ R ^ and r(U 2, H2) = < S2; R2 > are given, then the group F(X, H) is isonıorphic to the group defined by the generators S, U and the relations R, R2 (J Rs . As a result of this, the sheaf H, especially the fundamental group (X, x) was easily calculated for any x G X.

Keywords

Seifert - Van Kampen, global, sections

References

• Communications, Series A1:Mathematics and Statistics