2-local unstable homotopy groups of indecomposable A₃² -complexes

2023/02/11 by Zhongjian Zhu, Zhu, Zhongjian, Jianzhong Pan +1
Mathematics · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2302.05591

openalex publication_date 2023/02/11 · openalex created_date 2023/02/15 · openalex updated_date 2026/07/28

Abstract

In this paper, we calculate the 2-local unstable homotopy groups of indecomposable A₃²-complexes. The main technique used is analysing the homotopy property of J(X,A), defined by B. Gray for a CW-pair (X,A), which is homotopy equivalent to the homotopy fibre of the pinch map X∪ CA→ ΣA.

Related

• The n+3, n+4 dimensional homotopy groups of A_n²-complexes
• The unstable homotopy groups of 2-cell complexes
• The relative James construction and its application to homotopy groups
• Homotopy classification of based maps between A_n²-complexes
• The second homotopy group in terms of colorings of locally finite models\n and new results on asphericity