ON FACTORIZATIONS OF THE SUBGROUPS OF SELF-HOMOTOPY EQUIVALENCES

Title & Authors
ON FACTORIZATIONS OF THE SUBGROUPS OF SELF-HOMOTOPY EQUIVALENCES
Shi, Yi-Yun; Zhao, Hao;

Abstract
For a pointed space X, the subgroups of self-homotopy equivalences $\small{Aut_{\sharp}_N(X)}$, $\small{Aut_{\Omega}(X)}$, $\small{Aut_*(X)}$ and $\small{Aut_{\Sigma}(X)}$ are considered, where $\small{Aut_{\sharp}_N(X)}$ is the group of all self-homotopy classes f of X such that $f_{\sharp} Keywords self-homotopy equivalences;wedge spaces;product spaces;loop spaces;suspension; Language English Cited by References 1. M. Arkowitz, The group of self-homotopy equivalences-a survey, Groups of selfe-quivalences and related topics (Montreal, PQ, 1988), 170-203, Lecture Notes in Math., 1425, Springer, Berlin, 1990 2. M. Arkowitz and G. Lupton, On finiteness of subgroups of self-homotopy equivalences, The Cech centennial (Boston, MA, 1993), 1-25, Contemp. Math., 181, Amer. Math. Soc., Providence, RI, 1995 3. M. Arkowitz and G. Lupton, On the nilpotency of subgroups of self-homotopy equivalences, Algebraic topology: new trends in localization and periodicity (Sant Feliu de Guixols, 1994), 1-22, Progr. Math., 136, Birkhauser, Basel, 1996 4. M. Arkowitz and K. Maruyama, Self-homotopy equivalences which induce the identity on homology, cohomology or homotopy groups, Topology Appl. 87 (1998), no. 2, 133-154 5. E. D. Farjoun and A. Zabrodsky, Unipotency and nilpotency in homotopy equivalences, Topology 18 (1979), no. 3, 187-197 6. Y. Felix and A. Murillo, A bound for the nilpotency of a group of self homotopy equivalences, Proc. Amer. Math. Soc. 126 (1998), no. 2, 625-627 7. P. J. Hilton, Homotopy Theory and Duality, Gordon and Breach Science Publishers, New York-London-Paris 1965 8. K. Maruyama, Localization of a certain subgroup of self-homotopy equivalences, Pacific J. Math. 136 (1989), no. 2, 293-301 9. K. Maruyama, Localization of self-homotopy equivalences inducing the identity on homology, Math. Proc. Cambridge Philos. Soc. 108 (1990), no. 2, 291-297 10. P. Pavesic, On the group Aut#($X_{1}\times$. . .$\timesX_{n}$), Topology Appl. 153 (2005), no. 2-3, 485-492 11. P. Pavesic, On the group$Aut_{\Omega}\$(X), Proc. Edinb. Math. Soc. (2) 45 (2002), no. 3, 673-680

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