JOURNAL BROWSE
Search
Advanced SearchSearch Tips
GOTTLIEB GROUPS AND SUBGROUPS OF THE GROUP OF SELF-HOMOTOPY EQUIVALENCES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
GOTTLIEB GROUPS AND SUBGROUPS OF THE GROUP OF SELF-HOMOTOPY EQUIVALENCES
Kim, Jae-Ryong; Oda, Nobuyuki; Pan, Jianzhong; Woo, Moo-Ha;
  PDF(new window)
 Abstract
Let be the subgroups of consisting of homotopy classes of self-homotopy equivalences that fix homotopy groups through the dimension of X and be the subgroup of that fix homology groups for all dimension. In this paper, we establish some connections between the homotopy group of X and the subgroup . We also give some relations between , as well as a generalized Gottlieb group , and a subset of [X, W]. Finally we establish a connection between the coGottlieb group of X and the subgroup of consisting of homotopy classes of self-homotopy equivalences that fix cohomology groups.
 Keywords
self-homotopy equivalences;Gottlieb groups;coGottlieb groups;
 Language
English
 Cited by
1.
Cocyclic element preserving pair maps and fibrations, Topology and its Applications, 2015, 191, 82  crossref(new windwow)
2.
The set of cyclic-element preserving maps, Topology and its Applications, 2013, 160, 6, 794  crossref(new windwow)
 References
1.
M. Arkowitz, G. Lupton, and A. Murillo, Subgroups of the group of self-homotopy equivalences, Contemporary Mathematics 274 (2001), 21-32 crossref(new window)

2.
M. Arkowitz and K. Maruyama, Self-homotopy equivalences which induce the identity on homology, cohomology or homotopy groups, Topology Appl. 87 (1998), no. 2, 133-154 crossref(new window)

3.
H. J. Baues, Homotopy type and homology, Clarendon Press, Oxford, 1996

4.
E. Dror and A. Zabrodsky, Unipotency and nilpotency in homotopy equivalences, Topology 18 (1979), no. 3, 187-197 crossref(new window)

5.
D. H. Gottlieb, Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729-756 crossref(new window)

6.
P. Hilton, Homotopy theory and duality, Gordon and Breach Science Publishers, New York-London Paris, 1965

7.
P. J. Kahn, Self-equivalences of (n-1)-connected 2n-manifolds, Math. Ann. 180 (1969), 26-47 crossref(new window)

8.
K. Maruyama, Localization of a certain subgroup of self-homotopy equivalences, Pacific J. Math. 136 (1989), no. 2, 293-301 crossref(new window)

9.
K. Maruyama, Localization of self-homotopy equivalences inducing the identity on ho- mology, Math. Proc. Cambridge Philos. Soc. 108 (1990), no. 2, 291-297 crossref(new window)

10.
K. Maruyama, Stability properties of maps between Hopf spaces, Q. J. Math. 53 (2002), no. 1, 47-57 crossref(new window)

11.
N. Oda, Pairings and copairings in the category of topological spaces, Publ. Res. Inst. Math. Sci. 28 (1992), no. 1, 83-97 crossref(new window)

12.
S. Oka, N. Sawashita, and M. Sugawara, On the group of self-equivalences of a mapping cone, Hiroshima Math. J. 4 (1974), 9-28

13.
J. W. Rutter, A homotopy classi¯cation of maps into an induced fibre space, Topology 6 (1967), 379-403 crossref(new window)

14.
K. Varadarajan, Generalised Gottlieb groups, J. Indian Math. Soc. 33 (1969), 141-164

15.
G. W. Whitehead, Elements of homotopy theory, Graduate texts in Mathematics 61, Springer-Verlag, New York Heidelberg Berlin, 1978

16.
M. H. Woo and J.-R. Kim, Certain subgroups and homotopy groups, J. Korean. Math. Soc. 21 (1984), no. 2, 109-120