Lecture Notes in Mathematics

Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture

Authors: Capraro, Valerio, Lupini, Martino

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  • Accessible to anyone with a graduate-level mathematical background
  • Includes many exercises to help the reader to learn quickly
  • Presents some outstanding open problems in group theory and operator algebras
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About this book

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.

Table of contents (3 chapters)

Table of contents (3 chapters)

Buy this book

eBook n/a
  • ISBN 978-3-319-19333-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
Softcover n/a
  • ISBN 978-3-319-19332-8
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2136
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-19333-5
DOI
10.1007/978-3-319-19333-5
Softcover ISBN
978-3-319-19332-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 151
Topics