Given a connected CW-space X, SN T(X) denotes the set of all homotopy types[X′] such that the Postnikov approximations X^((n)) and X′^((n)) are homotopy equivalent for all n. The main purpose of this paper is to sho...Given a connected CW-space X, SN T(X) denotes the set of all homotopy types[X′] such that the Postnikov approximations X^((n)) and X′^((n)) are homotopy equivalent for all n. The main purpose of this paper is to show that the set of all the same homotopy ntypes of the suspension of the wedges of the Eilenberg-MacL ane spaces is the one element set consisting of a single homotopy type of itself, i.e., SNT(Σ(K(Z, 2a_1) ∨ K(Z, 2a_2) ∨···∨ K(Z, 2a_k))) = * for a_1 < a_2 < ··· < a_k, as a far more general conjecture than the original one of the same n-type posed by McG ibbon and M?ller(in [McG ibbon, C. A. and M?ller, J. M., On infinite dimensional spaces that are rationally equivalent to a bouquet of spheres, Proceedings of the 1990 Barcelona Conference on Algebraic Topology, Lecture Notes in Math., 1509, 1992, 285–293].)展开更多
基金supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF,in short)funded by the Ministry of Education(No.NRF-2015R1D1A1A09057449)
文摘Given a connected CW-space X, SN T(X) denotes the set of all homotopy types[X′] such that the Postnikov approximations X^((n)) and X′^((n)) are homotopy equivalent for all n. The main purpose of this paper is to show that the set of all the same homotopy ntypes of the suspension of the wedges of the Eilenberg-MacL ane spaces is the one element set consisting of a single homotopy type of itself, i.e., SNT(Σ(K(Z, 2a_1) ∨ K(Z, 2a_2) ∨···∨ K(Z, 2a_k))) = * for a_1 < a_2 < ··· < a_k, as a far more general conjecture than the original one of the same n-type posed by McG ibbon and M?ller(in [McG ibbon, C. A. and M?ller, J. M., On infinite dimensional spaces that are rationally equivalent to a bouquet of spheres, Proceedings of the 1990 Barcelona Conference on Algebraic Topology, Lecture Notes in Math., 1509, 1992, 285–293].)
