CONSTRUCTION OF NEW Ω-SPECTRUM AND THEIR APPLICATIONS TO COHOMOLOGY THEORY - Rana, DrPravanjan Kumar; Mandal, Bhaskar (IJRDO -JOURNAL OF MATHEMATICS, 2023)
The aim of this paper is to construct a new Ω-spectrum associated with infinite symmetric product functor of connected CW-complexes and their application to cohomology theory. In this paper we studies all cohomology operation for the cohomology theory associated with new Ω-spectrum. More precisely we prove that: i) the abelian group of all cohomology operations of degree k for the cohomology theory H^*(6pt;A) is isomorphic to the group H^n+k(SP^∞(Σ^n Y);A) ; and ii) the graded abelian group of all stable cohomology operations of degree k for the cohomology theory H^*(;A) is isomorphic to the group H^n+k(SP^∞(Σ^n Y);