JOURNAL BROWSE
Search
Advanced SearchSearch Tips
COHOMOLOGY AND TRIVIAL GOTTLIEB GROUPS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
COHOMOLOGY AND TRIVIAL GOTTLIEB GROUPS
Lee, Kee-Young;
  PDF(new window)
 Abstract
This paper observes that the induced homomorphisms on cohomology groups by a cyclic map are trivial. For a CW-complex X, we use the fact to obtain some conditions of X so that the n-th Gottlieb group is trivial for an even positive integer n. As corollaries, for any positive integer m, we obtain $G_{2m}(S^{2m})\;
 Keywords
evaluation subgroup;Gottlieb group;cyclic map;
 Language
English
 Cited by
 References
1.
D. H. Gottlieb, Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729-755 crossref(new window)

2.
D. H. Gottlieb, Witness, transgressions, and the evaluation map, Indiana Univ. Math.J. 24 (1975) no. 9, 825-836 crossref(new window)

3.
S. -T. Hu, Homotopy theorey, Academic Press, New York, (1989)

4.
G. E. Lang, Evaluation subgroups of factor spaces, Paciffic. J. Math. 42 (1972), 701-709 crossref(new window)

5.
G. Lupton and S. Smith, Rationalized evaluation subgroups of a map and the rationalized G-sequence, Preprint

6.
A. T. Lundell, Concise tables of James numbers and some homotopy classical Lie groups and associated homogeneous spaces, Algebraic topology(1990), 250-272 Lecture Notes in Math. 1509, Springer, Berlin, (1992) crossref(new window)

7.
K. Y. Lee and M. H. Woo, The G-sequence and the !-homology of a CW-pair, Topology Appl. 52 (1993), no. 3, 221-236 crossref(new window)

8.
K. Y. Lee and M. H. Woo, Cyclic morphisms in the category of pairs and generalized G-sequences, J. Math. Kyoto Univ. 38 (1998), no. 2, 271-285

9.
K. Y. Lee and M. H. Woo, Cocyclic morphisms and dual G-sequences, Topology Appl. 116 (2001), no. 1, 123-136 crossref(new window)

10.
M. Mimura, Homotopy Theory of Lie groups, Handbook of Algebraic Topology, Elsevier Science B. V. (1995), 951-991

11.
J. Oprea, Gottlieb groups, group actions, fixed points and rational homotopy, Lecture Notes Series, Seoul national Univ. Research Inc. Math. Global Analysis Research center, Seoul 29 (1995)

12.
J. Siegel, G-spaces, W-spaces and H-spaces, Paciffic J. Math. 31 (1970), 209-214

13.
S. B. Smith, Rational evaluation subgroups, Math. Zeit. 221 (1996), no. 3, 387- 400 crossref(new window)

14.
E. Spanier, Algebraic Topology, McGraw-Hill Book Company, New York (1981)