[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j160602

THE GENERALIZED COGOTTLIEB GROUPS, RELATED ACTIONS AND EXACT SEQUENCES

Choi, Ho-Won (Department of Mathematics Korea University)
Kim, Jae-Ryong (Department of Mathematics Kookmin University)
Oda, Nobuyuki (Department of Applied Mathematics Faculty of Science Fukuoka University)

Publication Information

Journal of the Korean Mathematical Society / v.54, no.5, 2017 , pp. 1623-1639 More about this Journal

Abstract

The generalized coGottlieb sets are not known to be groups in general. We study some conditions which make them groups. Moreover, there are actions on the generalized coGottlieb sets which are different from known actions up to now. We give related exact sequence of the generalized coGottlieb sets. Using them, we obtain certain results related to the maps which preserve generalized coGottlieb sets.

Keywords

cocyclic map; coGottlieb group;

Citations & Related Records

Reference

1	M. Arkowitz, Introduction to Homotopy Theory, Universitext, Springer, New York, 2011.
2	M. Arkowitz, G. Lupton, and A. Murillo, Subgroups of the group of self-homotopy equivalences, Groups of homotopy self-equivalences and related topics (Gargnano, 1999), 21-32, Contemp. Math., 274, Amer. Math. Soc., Providence, RI, 2001.
3	D. H. Gottlieb, Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729-756. DOI
4	B. Gray, Homotopy Theory, Academic Press, 1975.
5	H. B. Haslam, G-spaces and H-spaces, Thesis, University of California at Irvine, 1969.
6	H. B. Haslam, G-spaces mod F and H-spaces mod F, Duke Math. J. 38 (1971), 671-679. DOI
7	J.-R. Kim and N. Oda, Cocyclic element preserving pair maps and fibrations, Topology Appl. 191 (2015), 82-96. DOI
8	K. L. Lim, Cocyclic maps and coevaluation subgroups, Canad. Math. Bull. 30 (1987), no. 1, 63-71. DOI
9	C. R. F. Maunder, Algebraic Topology, Cambridge University Press, 1980.
10	N. Oda, The homotopy set of the axes of pairings, Canad. J. Math. 42 (1990), no. 5, 856-868. DOI
11	Y. S. Yoon, The generalized dual Gottlieb sets, Topology Appl. 109 (2001), no. 2, 173-181. DOI
12	N. Oda, Pairings and copairings in the category of topological spaces, Publ. Res. Inst. Math. Sci. 28 (1992), no. 1, 83-97. DOI
13	K. Varadarajan, Generalised Gottlieb groups, J. Indian Math. Soc. 33 (1969), 141-164.
14	G. W. Whitehead, Elements of homotopy theory, Graduate texts in Mathematics 61, Springer-Verlag, New York Heidelberg Berlin, 1978.