New directions in locally compact groups

著者

• Caprace, Pierre-Emmanuel
• Monod, Nicolas

書誌事項

New directions in locally compact groups

edited by Pierre-Emmanuel Caprace, Nicolas Monod

（London Mathematical Society lecture note series, 447）

Cambridge University Press, 2018

• : pbk

注記

Includes bibliographical references and index

内容説明・目次

内容説明

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.

目次

• 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 Lukasz 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 Swiatoslaw 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 Francois Le Maitre
• 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.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BB25523881
• ISBN:
  • 9781108413121
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge
• ページ数/冊数: viii, 358 p.
• 大きさ: 23 cm
• 分類:
  • DC23 : 512.55
• 件名:
  • LCSH : Locally compact groups
• 親書誌ID:
  • BA0005393X