TY - JOUR
AU - Rana, DrPravanjan Kumar
AU - Mandal, Bhaskar
PY - 2023/01/10
Y2 - 2024/06/21
TI - CONSTRUCTION OF NEW $\Omega$-SPECTRUM AND THEIR APPLICATIONS TO COHOMOLOGY THEORY
JF - IJRDO -JOURNAL OF MATHEMATICS
JA - m
VL - 9
IS - 1
SE - Articles
DO - 10.53555/m.v9i1.5337
UR - https://ijrdo.org/index.php/m/article/view/5337
SP - 14-18
AB - 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);
ER -