[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b200352

RELATIVE SELF-CLOSENESS NUMBERS

Yamaguchi, Toshihiro (Faculty of Education Kochi University)

Publication Information

Bulletin of the Korean Mathematical Society / v.58, no.2, 2021 , pp. 445-449 More about this Journal

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.

Keywords

Self-homotopy equivalence; fibration; relative self-closeness number; Sullivan model;

Citations & Related Records

Reference

1	P. A. Griffiths and J. W. Morgan, Rational homotopy theory and differential forms, Progress in Mathematics, 16, Birkhauser, Boston, MA, 1981.
2	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.
3	P. Hilton, G. Mislin, and J. Roitberg, Localization of nilpotent groups and spaces, North-Holland Publishing Co., Amsterdam, 1975.
4	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 DOI
5	D. Sullivan, Infinitesimal computations in topology, Inst. Hautes Etudes Sci. Publ. Math. No. 47 (1977), 269-331 (1978). DOI
6	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 DOI
7	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 DOI