On the Same n-Types for the Wedges of the Eilenberg-Maclane Spaces

作     者：Dae-Woong LEE 

作者机构：Department of Mathematics Institute of Pure and Applied Mathematics Chonbuk National University 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2016年第37卷第6期

页      面：951-962页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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) 

主　　题：Same n-type Aut Basic Whitehead product Samelson product Bott-Samelson theorem Tensor algebra Cartan-Serre theorem Hopf-Thom theorem 

摘      要：Given a connected CW-space X, SNT（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 n- types of the suspension of the wedges of the Eilenberg-MacLane spaces is the one element set consisting of a single homotopy type of itself, i.e., SNT（Σ（K（Z, 2a1） ∨ K（Z, 2a2）∨… ∨ K（Z,2ak））） = ＊ for a1 〈 a2 〈 … 〈 ak, as a far more general conjecture than the original one of the same n-type posed by McGibbon and Moller （in [McGibbon, C. A. and Moller, 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].）