A homotopical property of attractors

Rafael Ortega, Jaime Jorge Sánchez-Gabites

Abstract


We construct a 2-dimensional torus T ⊆ R3 having the property that it cannot be an attractor for any homeomorphism of R3. To this end we show that the fundamental group of the complement of an attractor has certain finite generation property that the complement of T does not have.

Keywords


Attractor; homeomorphism; fundamental group; finitely generated; Antoine necklace; Antoine sphere

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References


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