Abstract
We construct a $2$-dimensional torus $\mathcal{T} \subseteq \mathbb{R}^3$ having the property that it cannot be an attractor for any homeomorphism of $\mathbb{R}^3$. To this end we show that the fundamental group of the complement of an attractor has certain finite generation property that the complement of $\mathcal{T}$ does not have.
Citation
Rafael Ortega. Jaime J. Sánchez-Gabites. "A homotopical property of attractors." Topol. Methods Nonlinear Anal. 46 (2) 1089 - 1106, 2015. https://doi.org/10.12775/TMNA.2015.082
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