New Directions in Locally Compact Groups

ISBN-13: 9781108413121 / Angielski / Miękka / 2018 / 366 str.

Pierre-Emmanuel Caprace; Nicolas Monod

Opis

A snapshot of the major renaissance happening today in the study of locally compact groups and their many applications.

Spis treści

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.