Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture

Language: English

Published by Springer, Springer Okt 2015, 2015

3319193325 / 9783319193328

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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 164 pp. Englisch.

Seller Inventory # 9783319193328

Title
Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture
Author
Valerio Capraro
Publisher
Springer, Springer Okt 2015
Publication year
2015
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3319193325
ISBN 13
9783319193328
Item weight
260 grams
Dimensions
235x155x10 mm

buchversandmimpf2000

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