Amenability of Discrete Groups by Examples

Released on by Kate Juschenko
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  • Amenability of Discrete Groups by Examples Book Detail

  • Author : Kate Juschenko
  • Release Date : 2022-06-30
  • Publisher : American Mathematical Society
  • Genre : Mathematics
  • Pages : 180
  • ISBN 13 : 1470470322
  • File Size : 49,49 MB
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Amenability of Discrete Groups by Examples by Kate Juschenko PDF Summary

Book Description: The main topic of the book is amenable groups, i.e., groups on which there exist invariant finitely additive measures. It was discovered that the existence or non-existence of amenability is responsible for many interesting phenomena such as, e.g., the Banach-Tarski Paradox about breaking a sphere into two spheres of the same radius. Since then, amenability has been actively studied and a number of different approaches resulted in many examples of amenable and non-amenable groups. In the book, the author puts together main approaches to study amenability. A novel feature of the book is that the exposition of the material starts with examples which introduce a method rather than illustrating it. This allows the reader to quickly move on to meaningful material without learning and remembering a lot of additional definitions and preparatory results; those are presented after analyzing the main examples. The techniques that are used for proving amenability in this book are mainly a combination of analytic and probabilistic tools with geometric group theory.

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