Algebraic computation of short exact sequence and topological invariants using K-theory in general ring of classification spaces

The objective of this study is to calculate the K-Cohomology invariants of certain classification spaces of homotopy groups in short exact sequences, where the computation is done using properties of the K-theoretical features. For these packages we use various applications including K-theory Algebra, which transformed the theory of operator algebra from a smaller branch of functional analysis into a topic with deep and wide application areas in all algebra and topology in mathematics.