Realizability of the group of rational self-homotopy equivalences

2010/10/07 by Mahmoud Benkhalifa, Benkhalifa, Mahmoud · 1 citation
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT

paper · pdf · doi:10.48550/arxiv.1010.1441

arxiv created 2010/10/07 · openalex publication_date 2010/10/07 · arxiv updated 2010/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a 1-connected CW-complex X, let E(X) denote the group of homotopy classes of self-homotopy equivalences of X. The aim of this paper is to prove that, for every n∈\Bbb N, there exists a 1-connected rational CW-complex X_n such that E(X_n)≅ \underset2ⁿ⁺¹. times\underbrace\Bbb Z₂⊕... \Bbb ⊕ \Bbb Z₂.

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