CERTAIN GENERALIZATIONS OF G-SEQUENCES AND THEIR EXACTNESS

Title & Authors
CERTAIN GENERALIZATIONS OF G-SEQUENCES AND THEIR EXACTNESS
Lee, Kee-Young; Woo, Moo-Ha; Zhao, Xuezhi;

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;
Language
English
Cited by
1.
GOTTLIEB SUBSETS WITH RESPECT TO A MORPHISM IN THE CATEGORY OF PAIRS,;;

대한수학회보, 2010. vol.47. 6, pp.1311-1327
1.
GOTTLIEB SUBSETS WITH RESPECT TO A MORPHISM IN THE CATEGORY OF PAIRS, Bulletin of the Korean Mathematical Society, 2010, 47, 6, 1311
References
1.
R. Brooks, Certain subgroups of the fundamental group and the number of roots of f(x) = a, Amer. J. Math. 95 (1973), 720-728

2.
R. F. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresman and Co., Glenview, Ill.-London 1971

3.
D. Gottlieb, A certain subgroup of the fundamental group, Amer. J. Math. 87 (1965), 840-856

4.
D. Gottlieb, Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729-756

5.
D. Gottlieb, Covering transformations and universal fibrations, Illinois J. Math. 13 (1969), 432-437

6.
B. Jiang, Estimation of the Nielsen numbers, Acta Math. Sinica 14 (1964), 304-312

7.
B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemporary Mathematics, 14. American Mathematical Society, Providence, R.I., 1983

8.
T. H. Kiang, The Theory of Fixed Point Classes, Translated from the second Chinese edition. Springer-Verlag, Berlin; Science Press, Beijing, 1989

9.
K. Lee and M. Woo, The G-sequence and the $\omega$-homology of CW-pair, Topology Appl. 52 (1993), no. 3, 221-236

10.
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

11.
J. Pak and M. Woo, A remark on G-sequences, Math. Japon. 46 (1997), no. 3, 427-432

12.
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

13.
M. Woo and J. Kim, Certain subgroups of homotopy groups, J. Korean Math. Soc. 21 (1984), no. 2, 109-120

14.
M. Woo and K. Lee, On the relative evaluation subgroups of a CW-pair, J. Korean Math. Soc. 25 (1988), no. 1, 149-160

15.
M. Woo and Y. Yoon, Certain subgroups of homotopy groups of a transformation group, J. Korean Math. Soc. 20 (1983), no. 2, 223-233

16.
X. Zhao, Realization of fixed point sets, Acta Math. Sinica (N.S.) 12 (1996), no. 1, 71-76