SOME ADVANCED RESULTS ON CO-HOMOLOGY GROUP OF K(Z,n)
Hero Mawlood Salih
Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah, Iraq.
Hardi Nasradin Aziz
Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah, Iraq.
Hardi Ali Shareef
Department of Mathematics, College of Science, University of Sulaimani, Sulaymaniyah, Iraq.
E-mail: hero.salh@univsul.edu.iq1, harde.aziz@univsul.edu.iq and hardy.shareef@univsul.edu.iq
*Corresponding author: hardy.shareef@univsul.edu.iq
*ORCID ID: 0000-0003-2798-1921
Abstract:
The purpose of having the serre- spectral sequence is to compute co-homology, in particular when we have a fibration F → E → B. This study discusses Eilenberg macLane spaces and their co-homology groups. We use the method of spectral sequence to construct the cohomology of K(Z,n), and respectively we can express topological groups of (n − 1)- connected space X by K(Z,n). The main purpose of this paper is to compute co-homology groups of Eilenberg-MacLane space K(Z,6) and K(Z,7).
Key words: Homology group, Co-homology group, Spectral sequence, Serre spectral sequence.