# EVALUATION SUBGROUPS AND CELLULAR EXTENSIONS OF CW-COMPLEXES

• Lee, Kee-Young (Department of Mathematics, Taejon National University of Technology, Taejon 300) ;
• Woo, Moo-Ha (Department of Mathematics Education, Korea University, Seoul 136)
• Published : 1995.02.01

#### Abstract

D. H. Gottlieb [1, 2] studied the subgroups $G_n(X)$ of homotopy groups $\pi_n(X)$. In [5, 7, 10], the authors introduced subgroups $G_n(X, A)$ and $G_n^{Rel}(X, A) of \pi_n(X)$ and $\pi_n(X, A)$ respectively and showed that they fit together into a sequence $$\cdots \to G_n(A) \longrightarrow^{i_*} G_n(X, A) \longrightarrow^{j_*} G_n^{Rel}(X, A) \longrightarrow^\partial$$ $$\cdots \to G_1^{Rel}(X, A) \to G_0(A) \ to G_0(X, A)$$ where $i_*, j_*$ and \partial\$ are restrictions of the usual homomorphisms of the homotopy sequence $$\cdot \to^\partial \pi_n(A) \longrightarrow^{i_*} \pi_n(X) \longrightarrow^{j_*} \pi_n(X, A) \to \cdot \to \pi_0(A) \to \pi_0(X)$$.