Certain maps preserving self-homotopy equivalences

2015/06/30 by Jinho Lee, Jin-ho Lee, Lee, Jin-ho +2
Mathematics · #55P10 #55P62 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:55P10 #msc:55P62

paper · pdf · doi:10.48550/arxiv.1506.09126

openalex publication_date 2015/06/30 · arxiv created 2016/08/14 · arxiv updated 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let E(X) be the group of homotopy classes of self homotopy equivalences for a connected CW complex X. We observe two classes of maps E-maps and co-E-maps. They are defined as the maps X→ Y that induce the homomorphisms E(X)→ E( Y) and E(Y)→ E(X), respectively. We give some rationalized examples related to spheres, Lie groups and homogeneous spaces by using Sullivan models. Furthermore, we introduce an E-equivalence relation between rationalized spaces X_ℚ and Y_ℚ as a geometric realization of an isomorphism E(X_ℚ)≅ E(Y_ℚ).

Citations

• Realizability of the group of rational self-homotopy equivalences

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