Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture: 2136 (Lecture Notes in Mathematics) - Tapa blanda

Capraro, Valerio; Lupini, Martino

 
9783319193328: Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture: 2136 (Lecture Notes in Mathematics)
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ISBN 10: 3319193325 ISBN 13: 9783319193328
Editorial: Springer, 2015

Sinopsis

This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture. These notions, as well as the proofs of many results, are presented in the framework of model theory for metric structures. This point of view, rarely explicitly adopted in the literature, clarifies the ideas therein, and provides additional tools to attack open problems.

Sofic and hyperlinear groups are countable discrete groups that can be suitably approximated by finite symmetric groups and groups of unitary matrices. These deep and fruitful notions, introduced by Gromov and Radulescu, respectively, in the late 1990s, stimulated an impressive amount of research in the last 15 years, touching several seemingly distant areas of mathematics including geometric group theory, operator algebras, dynamical systems, graph theory, and quantum information theory. Several long-standing conjectures, still open for arbitrary groups, are now settled for sofic or hyperlinear groups.

The presentation is self-contained and accessible to anyone with a graduate-level mathematical background. In particular, no specific knowledge of logic or model theory is required. The monograph also contains many exercises, to help familiarize the reader with the topics present.

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Reseña del editor

This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture. These notions, as well as the proofs of many results, are presented in the framework of model theory for metric structures. This point of view, rarely explicitly adopted in the literature, clarifies the ideas therein, and provides additional tools to attack open problems.

Sofic and hyperlinear groups are countable discrete groups that can be suitably approximated by finite symmetric groups and groups of unitary matrices. These deep and fruitful notions, introduced by Gromov and Radulescu, respectively, in the late 1990s, stimulated an impressive amount of research in the last 15 years, touching several seemingly distant areas of mathematics including geometric group theory, operator algebras, dynamical systems, graph theory, and quantum information theory. Several long-standing conjectures, still open for arbitrary groups, are now settled for sofic or hyperlinear groups.

The presentation is self-contained and accessible to anyone with a graduate-level mathematical background. In particular, no specific knowledge of logic or model theory is required. The monograph also contains many exercises, to help familiarize the reader with the topics present.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer
Año de publicación
2015
Idioma
Inglés
ISBN 10 
3319193325
ISBN 13 
9783319193328
Encuadernación
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Número de edición
1
Número de páginas
164
Contacto del fabricante
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Darmstadt
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Alemania

Otras ediciones populares con el mismo título

9783319193342: Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture

Edición Destacada

ISBN 10:  3319193341 ISBN 13:  9783319193342
Editorial: Springer, 2015
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