Homology, Homotopy and Applications

Volume 21 (2019)

Number 2

Periodic problem on homotopy groups of Chang complexes $C^{n+2,r}_{r}$

Pages: 363 – 375

DOI: https://dx.doi.org/10.4310/HHA.2019.v21.n2.a20

Authors

Zhongjian Zhu (College of Mathematics, Physics and Electronic Information Engineering, Wenzhou University, Wenzhou, Zhejiang, China)

Pengcheng Li (Academy of Mathematics and Systems Science, Chinese Academy of Sciences; and University of Chinese Academy of Sciences, Beijing, China)

Jianzhong Pan (Hua Loo-Keng Key Mathematical Laboratory, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences; and University of Chinese Academy of Sciences, Beijing, China)

Abstract

In this paper, we find new examples, namely one class of Chang complexes $C^{n+2,r}_{r}$, such that their stable homotopy groups are direct summands of their unstable homotopy groups.

Keywords

Chang-complex, smash product, loop space, decomposition, homotopy group

2010 Mathematics Subject Classification

55P10, 55P35, 55Q05

Full Text (PDF format)

The first author was partially supported by National Natural Science Foundation of China (Grant No. 11701430); the second and third authors were partially supported by National Natural Science Foundation of China (Grant No. 11661131004, 11131008).

Received 11 December 2018

Received revised 17 March 2019

Accepted 18 April 2019

Published 5 June 2019