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

2009/02/10 by Paul Fabel, Fabel, Paul
Engineering · Mathematics · #55Q52 #Advanced Numerical Analysis Techniques #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematics and Applications #math.AT #msc:55Q52

paper · pdf · doi:10.48550/arxiv.0902.1723

25 pages - some reorganization and minor editing from 1st version

openalex publication_date 2009/02/10 · arxiv created 2009/03/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A planar compactum with connected complement can be an embedded in a cellular continuum by attaching a null sequence of arcs. Two based maps f and g from a planar Peano continuum X to a planar set Y are homotopic iff f and g induce the same homomorphism between fundamental groups.

Related

• Homotopy type of planar continua
• The homotopy dimension of codiscrete subsets of the 2-sphere
• Concerning Fundamental Groups of Locally Connected Subsets of the Plane
• A model for planar compacta and rational Julia sets
• Peano Model for Planar Compacta and a Lemma by Beardon