Composition of Steenrod Square Operations on Symmetry Cohomomology of Topological Spaces with Applications

Dr. Yousif Altayeb
Department of Management
Information Systems
College of Business and Economics
Qassim University
Buraydah 51452, Saudi Arabia
عنوان البريد الإلكتروني هذا محمي من روبوتات السبام. يجب عليك تفعيل الجافاسكربت لرؤيته.

Key words:  Steen rod square, power operation, vector bundles, characteristic classes, cohomology theory, homology theory, convex function

  Abstract
 This paper aims to combine the constructions of classical Steenrod operations, such as homogeneity operations on polynomials on ZP and cohomology of topological spaces, where p is a prime integer. Cohomological processes are natural-to-natural transformations, and then we define the characteristics of Steenrod processes and we define what we are aiming for, so we will proceed with the construction. This will be used space-wise, and then make sure that the build we're doing implements Steenrod operations; in the odd case, there won't be sufficient space in the project for this. We have included several immediate applications, and then we will briefly discuss the build we have completed and propose that further development should continue from this point. Lastly, we have some necessary details and calculations to ensure the smooth functioning of the build in the field