2021/06/10 by keyvan Salehi, Salehi, Keyvan
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2106.05448
openalex publication_date 2021/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We are familiar with properties and structure of topological spaces. One of the powerful tools, which help us to figure out the structure of topological spaces is (Leray- Serre) spectral sequence. Although Eilenberg-Maclane space plays important roles in topology, and respectively geometry. Actually finding cohomology groups of this space can be useful for classifying spaces, and also homotopy groups structure of these groups. This paper discusses how to compute cohomology groups of Eilenberg-Maclane spaces K(ℤ, 4) and K(ℤ, 5) (cohomology degree less than 11). Furthermore we give the method to find cohomology groups of K(ℤ, n). Some proofs are given to the basic facts about cohomology group of K(ℤ, 5) and K(ℤ,4).