CONSTRUCTION OF NEW $\Omega$-SPECTRUM AND THEIR APPLICATIONS TO COHOMOLOGY THEORY

Abstract

The aim of this paper is to construct a new $\Omega-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 $\Omega$-spectrum.\\More precisely we prove that:\\i) the abelian group of all cohomology operations of degree k for the cohomology theory $H^*(\hspace{6pt};\underline{A})$ is isomorphic to the group $H^{n+k}(SP^{\infty}(\Sigma^n Y);\underline{A})$ ; and \\ii) the graded abelian group of all stable cohomology operations of degree k for the cohomology theory $H^*(;\underline{A})$ is isomorphic to the group $ \varprojlim H^{n+k}(SP^{\infty}(\Sigma^n Y);