[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2008.45.1.119

CERTAIN GENERALIZATIONS OF G-SEQUENCES AND THEIR EXACTNESS

Lee, Kee-Young (DEPARTMENT OF INFORMATION AND MATHEMATICS KOREA UNIVERSITY)
Woo, Moo-Ha (DEPARTMENT OF MATHEMATICS KOREA UNIVERSITY)
Zhao, Xuezhi (DEPARTMENT OF MATHEMATICS CAPITA NORMAL UNIVERSITY)

Publication Information

Bulletin of the Korean Mathematical Society / v.45, no.1, 2008 , pp. 119-131 More about this Journal

Abstract

In this paper, we generalize the Gottlieb groups and the related G-sequence of those groups, and present some sufficient conditions to ensure the exactness or non-exactness of G-sequences at some terms. We also give some applications of the exactness or non-exactness of G-sequences. Especially, we show that the non-exactness of G-sequences implies the non-triviality of homotopy groups of some function spaces.

Keywords

Gottlieb group; G-sequence; homotopy group;

Citations & Related Records

Times Cited By Web Of Science : 1 (Related Records In Web of Science)
Times Cited By SCOPUS : 1

Reference
Cited By SCOPUS

1	D. Gottlieb, A certain subgroup of the fundamental group, Amer. J. Math. 87 (1965), 840-856 DOI ScienceOn
2	D. Gottlieb, Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729-756 DOI ScienceOn
3	D. Gottlieb, Covering transformations and universal fibrations, Illinois J. Math. 13 (1969), 432-437
4	B. Jiang, Estimation of the Nielsen numbers, Acta Math. Sinica 14 (1964), 304-312
5	B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemporary Mathematics, 14. American Mathematical Society, Providence, R.I., 1983
6	R. Brooks, Certain subgroups of the fundamental group and the number of roots of f(x) = a, Amer. J. Math. 95 (1973), 720-728 DOI ScienceOn
7	X. Zhao, Realization of fixed point sets, Acta Math. Sinica (N.S.) 12 (1996), no. 1, 71-76 DOI
8	M. Woo and K. Lee, On the relative evaluation subgroups of a CW-pair, J. Korean Math. Soc. 25 (1988), no. 1, 149-160
9	J. Pan, X. Shen, and M. Woo, The G-sequence of a map and its exactness, J. Korean Math. Soc. 35 (1998), no. 2, 281-294 과학기술학회마을
10	M. Woo and J. Kim, Certain subgroups of homotopy groups, J. Korean Math. Soc. 21 (1984), no. 2, 109-120
11	T. H. Kiang, The Theory of Fixed Point Classes, Translated from the second Chinese edition. Springer-Verlag, Berlin; Science Press, Beijing, 1989
12	M. Woo and Y. Yoon, Certain subgroups of homotopy groups of a transformation group, J. Korean Math. Soc. 20 (1983), no. 2, 223-233
13	R. F. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresman and Co., Glenview, Ill.-London 1971
14	K. Lee and M. Woo, The G-sequence and the $\omega$ -homology of CW-pair, Topology Appl. 52 (1993), no. 3, 221-236 DOI ScienceOn
15	G. Lupton and S. Smith, Rationalized evaluation subgroups of a map. I. Sullivan models, derivations and G-sequences, J. Pure Appl. Algebra 209 (2007), no. 1, 159-171 DOI ScienceOn
16	J. Pak and M. Woo, A remark on G-sequences, Math. Japon. 46 (1997), no. 3, 427-432