图书简介
This collection of expository articles provides an overview of the major renaissance happening today in the study of locally compact groups and their many connections to other areas of mathematics, including geometric group theory, measured group theory and rigidity of lattices. For researchers and graduate students.
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 focal hyperbolic groups Yves de Cornulier; 20. Future directions in locally compact groups: a tentative problem list Pierre-Emmanuel Caprace and Nicolas Monod; Index.
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