Homotopy type of planar continua

2017/09/26 by Curtis Kent, Kent, Curtis
Mathematics · #Advanced Topics in Algebra #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1709.09211

openalex publication_date 2017/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the homotopy type of a map from a Peano continuum into a planar or one-dimensional space is determined by the induced homomorphism of fundamental groups. This provides a new proof that planar sets are aspherical and is used to prove that two planar or one-dimensional Peano continua are homotopy equivalent if and only if they have isomorphic fundamental groups.

Related

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• Embedding planar compacta in planar continua with application: homotopic maps between planar Peano continua are characterized by the fundamental group homomorphism
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• Peano dimension of fundamental groups
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