Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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RELATIVE SELF-CLOSENESS NUMBERS

  • Received : 2020.04.16
  • Accepted : 2020.12.30
  • Published : 2021.03.31
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Abstract

We define the relative self-closeness number N��(g) of a map g : X → Y, which is a generalization of the self-closeness number N��(X) of a connected CW complex X defined by Choi and Lee [1]. Then we compare N��(p) with N��(X) for a fibration $X{\rightarrow}E{\rightarrow\limits^p}Y$. Furthermore we obtain its rationalized result.

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References

  1. H. W. Choi and K. Y. Lee, Certain numbers on the groups of self-homotopy equivalences, Topology Appl. 181 (2015), 104-111. https://doi.org/10.1016/j.topol.2014.12.004
  2. Y. Felix, S. Halperin, and J.-C. Thomas, Rational Homotopy Theory, Graduate Texts in Mathematics, 205, Springer-Verlag, New York, 2001. https://doi.org/10.1007/978-1-4613-0105-9
  3. P. A. Griffiths and J. W. Morgan, Rational homotopy theory and differential forms, Progress in Mathematics, 16, Birkhauser, Boston, MA, 1981.
  4. S. Halperin, Rational homotopy and torus actions, in Aspects of topology, 293-306, London Math. Soc. Lecture Note Ser., 93, Cambridge Univ. Press, Cambridge, 1985.
  5. P. Hilton, G. Mislin, and J. Roitberg, Localization of nilpotent groups and spaces, North-Holland Publishing Co., Amsterdam, 1975.
  6. N. Oda and T. Yamaguchi, Self-maps of spaces in fibrations, Homology Homotopy Appl. 20 (2018), no. 2, 289-313. https://doi.org/10.4310/hha.2018.v20.n2.a15
  7. D. Sullivan, Infinitesimal computations in topology, Inst. Hautes Etudes Sci. Publ. Math. No. 47 (1977), 269-331 (1978). https://doi.org/10.1007/BF02684341