Kompakt irtibatlı lie grupları Üzerinde demetler ve homotopi normalite

Abstract

Bu tez bes bolumden olusmaktadir. Birinci bolum giris kismina ayrilmistir. Ikinci bolumde tez icin gerekli olan tarif ve teoremler verilmistir. Ucuncu bolumde, homotopi ve demet teorisi ele alinmistir. Dorduncu bolumde, Lie gruplari ve manifoldlar incelenerek bazi sonuclar takdim edilmistir. Son olarak besinci bolumde ise Kompakt Irtibatli Lie gruplari uzerinde demetler teskil edilerek bazi karakterizasyonlar verilmis ve Homotopi Normalite tarif edilerek demet morfizmi altinda homotopi normalligin korundugu gosterilmistir.Abstract This thesis consists of five chapters. The first chapter has been devoted to the introduction. In the second chapter, it was given fundamental definitions and theorems that will be needed for this thesis. In the third chapter, homotopy and sheaf theory were included. In the fourth chapter, investigating Lie groups some corollaries were established. Finally in the fifth chapter, by constructing sheaves on compact connected Lie groups, some characterizations were given and by defining homotopy normality, it was shown that homotopy normality is preserved under sheaves morphisms.