Topological Methods in Nonlinear Analysis

A homotopical property of attractors

Rafael Ortega and Jaime J. Sánchez-Gabites

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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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 46, Number 2 (2015), 1089-1106.

Dates
First available in Project Euclid: 21 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1458588675

Digital Object Identifier
doi:10.12775/TMNA.2015.082

Mathematical Reviews number (MathSciNet)
MR3494984

Zentralblatt MATH identifier
1362.37036

Citation

Ortega, Rafael; Sánchez-Gabites, Jaime J. A homotopical property of attractors. Topol. Methods Nonlinear Anal. 46 (2015), no. 2, 1089--1106. doi:10.12775/TMNA.2015.082. https://projecteuclid.org/euclid.tmna/1458588675


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