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New Directions in Locally Compact Groups

$79.00 ( ) USD

Part of London Mathematical Society Lecture Note Series

George Willis, Marc Burger, Romain Tessera, John S. Wilson, Helge Gloeckner, Benjamin Klopsch, Alejandra Garrido, Yair Glasner, Stephan Tornier, Colin Reid, Łukasz Garncarek, Nir Lazarovich, Albrecht Brehm, Maxime Gheysens, Adrien Le Boudec, Rafaela Rollin, Phillip Wesolek, Światosław Gal, Laurent Bartholdi, Tsachik Gelander, Roman Sauer, Thibaut Dumont, Dennis Gulko, Morgan Cesa, François Le Maître, John S. Wilson, David Hume, Thierry Stulemeijer, Yves de Cornulier, Pierre-Emmanuel Caprace, Nicolas Monod
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  • Date Published: January 2018
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781108351942

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About the Authors
  • This collection of expository articles by a range of established experts and newer researchers provides an overview of the recent developments in the theory of locally compact groups. It includes introductory articles on totally disconnected locally compact groups, profinite groups, p-adic Lie groups and the metric geometry of locally compact groups. Concrete examples, including groups acting on trees and Neretin groups, are discussed in detail. An outline of the emerging structure theory of locally compact groups beyond the connected case is presented through three complementary approaches: Willis' theory of the scale function, global decompositions by means of subnormal series, and the local approach relying on the structure lattice. An introduction to lattices, invariant random subgroups and L2-invariants, and a brief account of the Burger–Mozes construction of simple lattices are also included. A final chapter collects various problems suggesting future research directions.

    • Presents the most recent activity in the field, helping the reader identify the current 'hotspots'
    • Provides a global view of the most important topics, made accessible through specific cases
    • Includes the necessary mathematical treatments to allow the reader to dive into the more specialised literature, using this book as a guide
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    Product details

    • Date Published: January 2018
    • format: Adobe eBook Reader
    • isbn: 9781108351942
    • contains: 16 b/w illus.
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Foreword George Willis
    1. On the role of totally disconnected groups in the structure of locally compact groups Marc Burger
    2. Locally compact groups as metric spaces Romain Tessera
    3. A short primer on profinite groups John S. Wilson
    4. Lectures on Lie groups over local fields Helge Gloeckner
    5. Abstract quotients of profinite groups, after Nikolov and Segal Benjamin Klopsch
    6. Automorphism groups of trees: generalities and prescribed local actions Alejandra Garrido, Yair Glasner and Stephan Tornier
    7. Simon Smith's construction of an uncountable family of simple, totally disconnected, locally compact groups Colin Reid and George Willis
    8. The Neretin groups Łukasz Garncarek and Nir Lazarovich
    9. The scale function and tidy subgroups Albrecht Brehm, Maxime Gheysens, Adrien Le Boudec and Rafaela Rollin
    10. Contraction groups and the scale Phillip Wesolek
    11. The Bader–Shalom normal subgroup theorem Światosław Gal
    12. Burger–Mozes' simple lattices Laurent Bartholdi
    13. A lecture on invariant random subgroups Tsachik Gelander
    14. L2-Betti number of discrete and non-discrete groups Roman Sauer
    15. Minimal normal closed subgroups in compactly generated tdlc groups Thibaut Dumont and Dennis Gulko
    16. Elementary totally disconnected locally compact groups, after Wesolek Morgan Cesa and François Le Maître
    17. The structure lattice of a totally disconnected locally compact group John S. Wilson
    18. The centraliser lattice David Hume and Thierry Stulemeijer
    19. On the quasi-isometric classification of locally compact groups Yves de Cornulier
    20. Future directions in locally compact groups: a tentative problem list Pierre-Emmanuel Caprace and Nicolas Monod
    Index.

  • Editors

    Pierre-Emmanuel Caprace, Université Catholique de Louvain, Belgium
    Pierre-Emmanuel Caprace is a member of the Institute of Research in Mathematics and Physics (IRMP) at the Catholic University of Leuven, Belgium. His joint work with his co-author, Nicolas Monod, received the Berwick Prize from the London Mathematical Society in 2015.

    Nicolas Monod, École Polytechnique Fédérale de Lausanne
    Nicolas Monod is a professor and director of the research chair EGG at �cole Polytechnique F�d�rale de Lausanne. He is also the Director of the Bernoulli Center (CIB). His joint work with his co-author, Pierre-Emmanuel Caprace, received the Berwick Prize from the London Mathematical Society in 2015.

    Contributors

    George Willis, Marc Burger, Romain Tessera, John S. Wilson, Helge Gloeckner, Benjamin Klopsch, Alejandra Garrido, Yair Glasner, Stephan Tornier, Colin Reid, Łukasz Garncarek, Nir Lazarovich, Albrecht Brehm, Maxime Gheysens, Adrien Le Boudec, Rafaela Rollin, Phillip Wesolek, Światosław Gal, Laurent Bartholdi, Tsachik Gelander, Roman Sauer, Thibaut Dumont, Dennis Gulko, Morgan Cesa, François Le Maître, John S. Wilson, David Hume, Thierry Stulemeijer, Yves de Cornulier, Pierre-Emmanuel Caprace, Nicolas Monod

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