Borel superrigidity and the classification problem for the torsion-free abelian groups of finite rank

• Autores: Simon Thomas
• Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé , Javier Soria de Diego , Juan Luis Varona Malumbres , Joan Verdera , Vol. 2, 2006, ISBN 978-3-03719-022-7, págs. 93-116
• Idioma: inglés
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• Resumen

  • In 1937, Baer solved the classification problem for the torsion-free abelian groups of rank 1. Since then, despite the efforts of many mathematicians, no satisfactory solution has been found of the classification problem for the torsion-free abelian groups of rank n . 2. So it is natural to ask whether the classification problem for the higher rank groups is genuinely difficult. In this article, I will explain how this question can be partially answered, using ideas from descriptive set theory and Zimmer�fs superrigidity theory.