• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.235-244
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• 1996

For a self-map f of a CW-pair (X, A), we introduce the G(f)-sequence of (X, A) which consists of subgroups of homotopy groups in the homotopy sequence of (X, A) and show some properties of the relative homotopy Jian groups. We also show a condition for the G(f)-sequence to be exact.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.709-715
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• 1997

For a fibration (E,B,p) with fiber F and a fiber map f, we show that if the inclusion $i : F \to E$ has a left homotopy inverse, then $G^f_n(E,F)$ is isomorphic to $G^f_n(F,E) \oplus \pi_n(B)$. In particular, by taking f as the identity map on E we have $G_n(E,F)$ is isomorphic to $G_n(F) \oplus \pi_n(B)$.