Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

AN EXTENSION OF GOTTLIEB GROUPS

  • Lee, Kee-Young (Department of Mathematics Taejon National University of Technology ) ;
  • Woo, Moo-Ha (Department of Mathematics Education Korea University )
  • Published : 1997.08.01
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Abstract

In this paper, we extend the Gottlieb groups of a space to the Gottlieb groups of a map and show some properties of those groups. Especially, We show the 2nd Gottlieb group of a map is contained in the center of the homotopy group of the map and show $G_n(F) = \pi_n(f)$ for an H-map f between H-spaces. We also show the Gottlieb subgroups $G_n(A), G_n(X) and G_n(f)$ make a sequence if the map $f : A \to X$ has a right homotopy inverse.

Keywords

References

  1. Amer. J. Math. v.87 A certain subgroup of the fundamental group D. H. Gottlieb
  2. Amer. J. Math. v.91 Evaluation subgroups of homotopy groups D. H. Gottlieb
  3. J. of Korean Math. Soc. v.21 Certain subgroups of homotopy groups J. R. Kim;M. H. Woo
  4. Topology and its application v.52 The G-sequence and ω-homology of a CW-pair K. Y. Lee;M. H. Woo