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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/12892

Title: The universal coefficient theorem for homology and cohomology: an enigma of computations
Authors: Nkrumah, Frank Kwarteng
Gyampoh, Samuel Amoh
Obeng-Denteh, William
Keywords: Abelian group
homology
cohomology
exact sequences
tensor product
homomorphism
isomorphism
torsion product
extension
Kiinneth formula and cross product
Issue Date: 30-May-2019
Publisher: Archives of Current Research International
Abstract: Computing the homology of a group is a fundamental question and can be a very difficult task. A complete understanding of all the homology groups of mapping class groups of surfaces and 3- manifolds remains out of reach at present time. It is imperative that we give the universal coefficient theorem the supposed needed attention. In this article, we study some product topologies as well as the kiinneth formula for computing the (co) homology group of product spaces. The paper begins with study on the algebraic background with specific definitions and extends into four theorems considered as the Universal Coefficient Theorem. Though this article does not prove the theorems, yet much is done on some properties of each of these theorems, which is enough for the calculation of (co) homology groups.
Description: An article published by Archives of Current Research International and also available at DOI: 10.9734/ACRI/2019/v17i430116
URI: http://hdl.handle.net/123456789/12892
Appears in Collections:College of Science

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