Homotopy classification of based maps between A_n²-complexes

2020/08/07 by Pengcheng Li, Li, Pengcheng
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2008.03049

Abstract

Let X,Y be (n-1)-connected finite pointed CW-complexes of dimension at most n+2, n≥ 3. In this paper we give elementary proofs of the abelian group structure of [X,Y] of homotopy classes of based maps from X to Y, which was due to Baues and Schmidt. Furthermore, we determine the explicit generators associated to [X,Y]. As an application, we compute certain (sub)groups of self-homotopy equivalences of certain Chang complexes.

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