New directions in locally compact groups /:
A snapshot of the major renaissance happening today in the study of locally compact groups and their many applications.
Gespeichert in:
| Weitere Verfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2018.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
447. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | A snapshot of the major renaissance happening today in the study of locally compact groups and their many applications. 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. |
| Beschreibung: | 1 online resource (viii, 358 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781108351942 1108351948 9781108332675 1108332676 |
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| 520 | |a A snapshot of the major renaissance happening today in the study of locally compact groups and their many applications. | ||
| 520 | |a 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. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a On the role of totally disconnected groups in the structure of locally compact groups / Burger -- Locally compact groups as metric spaces / Tessera --A short primer on profinite groups / Wilson -- Lectures on Lie groups over local fields / Glöckner -- Abstract quotients of profinite groups, after Nikolov and Segal / Klopsch -- Automorphism groups of trees: generalities and prescribed local actions / Garrido-Glasner-Tornier -- Simon Smith's construction of an uncountable family of simple, totally disconnected, locally compact groups / Reid-Willis -- The Neretin groups / Garncarek-Lazarovich -- The scale function and tidy subgroups / Brehm-Gheysens-Le Boudec-Rollin -- Contraction groups and the scale / Wesolek -- The Bader-Shalom normal subgroup theorem / Gal -- Burger-Mozes' simple lattices / Bartholdi -- A lecture on invariant random subgroups / Gelander -- L2-Betti number of discrete and non-discrete groups / Sauer -- Minimal normal closed subgroups in compactly generated tdlc groups / Dumont-Gulko -- Elementary totally disconnected locally compact groups, after Wesolek / Cesa-Le Maître -- The structure lattice of a totally disconnected locally compact group / Wilson -- The centraliser lattice / Hume-Stulemeijer -- On the quasi-isometric classification of locally compact groups / Cornulier -- Future directions in locally compact groups: a tentative problem list / Caprace-Monod. | |
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| 650 | 0 | |a Compact groups. |0 http://id.loc.gov/authorities/subjects/sh85029280 | |
| 650 | 6 | |a Groupes compacts. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 0 | 7 | |a Grupos compactos |2 embucm |
| 650 | 7 | |a Compact groups |2 fast | |
| 700 | 1 | |a Caprace, Pierre-Emmanuel, |d 1981- |e editor. |1 https://id.oclc.org/worldcat/entity/E39PBJxxbmhRh73cDHCV4f3G73 |0 http://id.loc.gov/authorities/names/n2008075091 | |
| 700 | 1 | |a Monod, Nicolas, |d 1973- |e editor. |1 https://id.oclc.org/worldcat/entity/E39PBJgt9G8RhfDRR6ydKgfjG3 |0 http://id.loc.gov/authorities/names/n2001006796 | |
| 758 | |i has work: |a New directions in locally compact groups (Text) |1 https://id.oclc.org/worldcat/entity/E39PCG749HQ9rmHK3Wqb6yTbVC |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |t New directions in locally compact groups. |d Cambridge, United Kingdom : Cambridge University Press, 2018 |z 9781108413121 |w (OCoLC)1005190571 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v 447. |0 http://id.loc.gov/authorities/names/n42015587 | |
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| contents | On the role of totally disconnected groups in the structure of locally compact groups / Burger -- Locally compact groups as metric spaces / Tessera --A short primer on profinite groups / Wilson -- Lectures on Lie groups over local fields / Glöckner -- Abstract quotients of profinite groups, after Nikolov and Segal / Klopsch -- Automorphism groups of trees: generalities and prescribed local actions / Garrido-Glasner-Tornier -- Simon Smith's construction of an uncountable family of simple, totally disconnected, locally compact groups / Reid-Willis -- The Neretin groups / Garncarek-Lazarovich -- The scale function and tidy subgroups / Brehm-Gheysens-Le Boudec-Rollin -- Contraction groups and the scale / Wesolek -- The Bader-Shalom normal subgroup theorem / Gal -- Burger-Mozes' simple lattices / Bartholdi -- A lecture on invariant random subgroups / Gelander -- L2-Betti number of discrete and non-discrete groups / Sauer -- Minimal normal closed subgroups in compactly generated tdlc groups / Dumont-Gulko -- Elementary totally disconnected locally compact groups, after Wesolek / Cesa-Le Maître -- The structure lattice of a totally disconnected locally compact group / Wilson -- The centraliser lattice / Hume-Stulemeijer -- On the quasi-isometric classification of locally compact groups / Cornulier -- Future directions in locally compact groups: a tentative problem list / Caprace-Monod. |
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-11-27T13:28:12Z |
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| series2 | London Mathematical Society lecture note series ; |
| spelling | New directions in locally compact groups / edited by Pierre-Emmanuel Caprace, Université Catholique de Louvain, Belgium ; Nicolas Monod, École Polytechnique Fédérale de Lausanne. Cambridge : Cambridge University Press, 2018. ©2018 1 online resource (viii, 358 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 447 A snapshot of the major renaissance happening today in the study of locally compact groups and their many applications. 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. Includes bibliographical references and index. On the role of totally disconnected groups in the structure of locally compact groups / Burger -- Locally compact groups as metric spaces / Tessera --A short primer on profinite groups / Wilson -- Lectures on Lie groups over local fields / Glöckner -- Abstract quotients of profinite groups, after Nikolov and Segal / Klopsch -- Automorphism groups of trees: generalities and prescribed local actions / Garrido-Glasner-Tornier -- Simon Smith's construction of an uncountable family of simple, totally disconnected, locally compact groups / Reid-Willis -- The Neretin groups / Garncarek-Lazarovich -- The scale function and tidy subgroups / Brehm-Gheysens-Le Boudec-Rollin -- Contraction groups and the scale / Wesolek -- The Bader-Shalom normal subgroup theorem / Gal -- Burger-Mozes' simple lattices / Bartholdi -- A lecture on invariant random subgroups / Gelander -- L2-Betti number of discrete and non-discrete groups / Sauer -- Minimal normal closed subgroups in compactly generated tdlc groups / Dumont-Gulko -- Elementary totally disconnected locally compact groups, after Wesolek / Cesa-Le Maître -- The structure lattice of a totally disconnected locally compact group / Wilson -- The centraliser lattice / Hume-Stulemeijer -- On the quasi-isometric classification of locally compact groups / Cornulier -- Future directions in locally compact groups: a tentative problem list / Caprace-Monod. Print version record. Compact groups. http://id.loc.gov/authorities/subjects/sh85029280 Groupes compacts. MATHEMATICS Algebra Intermediate. bisacsh Grupos compactos embucm Compact groups fast Caprace, Pierre-Emmanuel, 1981- editor. https://id.oclc.org/worldcat/entity/E39PBJxxbmhRh73cDHCV4f3G73 http://id.loc.gov/authorities/names/n2008075091 Monod, Nicolas, 1973- editor. https://id.oclc.org/worldcat/entity/E39PBJgt9G8RhfDRR6ydKgfjG3 http://id.loc.gov/authorities/names/n2001006796 has work: New directions in locally compact groups (Text) https://id.oclc.org/worldcat/entity/E39PCG749HQ9rmHK3Wqb6yTbVC https://id.oclc.org/worldcat/ontology/hasWork Print version: New directions in locally compact groups. Cambridge, United Kingdom : Cambridge University Press, 2018 9781108413121 (OCoLC)1005190571 London Mathematical Society lecture note series ; 447. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1694346 Volltext |
| spellingShingle | New directions in locally compact groups / London Mathematical Society lecture note series ; On the role of totally disconnected groups in the structure of locally compact groups / Burger -- Locally compact groups as metric spaces / Tessera --A short primer on profinite groups / Wilson -- Lectures on Lie groups over local fields / Glöckner -- Abstract quotients of profinite groups, after Nikolov and Segal / Klopsch -- Automorphism groups of trees: generalities and prescribed local actions / Garrido-Glasner-Tornier -- Simon Smith's construction of an uncountable family of simple, totally disconnected, locally compact groups / Reid-Willis -- The Neretin groups / Garncarek-Lazarovich -- The scale function and tidy subgroups / Brehm-Gheysens-Le Boudec-Rollin -- Contraction groups and the scale / Wesolek -- The Bader-Shalom normal subgroup theorem / Gal -- Burger-Mozes' simple lattices / Bartholdi -- A lecture on invariant random subgroups / Gelander -- L2-Betti number of discrete and non-discrete groups / Sauer -- Minimal normal closed subgroups in compactly generated tdlc groups / Dumont-Gulko -- Elementary totally disconnected locally compact groups, after Wesolek / Cesa-Le Maître -- The structure lattice of a totally disconnected locally compact group / Wilson -- The centraliser lattice / Hume-Stulemeijer -- On the quasi-isometric classification of locally compact groups / Cornulier -- Future directions in locally compact groups: a tentative problem list / Caprace-Monod. Compact groups. http://id.loc.gov/authorities/subjects/sh85029280 Groupes compacts. MATHEMATICS Algebra Intermediate. bisacsh Grupos compactos embucm Compact groups fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85029280 |
| title | New directions in locally compact groups / |
| title_auth | New directions in locally compact groups / |
| title_exact_search | New directions in locally compact groups / |
| title_full | New directions in locally compact groups / edited by Pierre-Emmanuel Caprace, Université Catholique de Louvain, Belgium ; Nicolas Monod, École Polytechnique Fédérale de Lausanne. |
| title_fullStr | New directions in locally compact groups / edited by Pierre-Emmanuel Caprace, Université Catholique de Louvain, Belgium ; Nicolas Monod, École Polytechnique Fédérale de Lausanne. |
| title_full_unstemmed | New directions in locally compact groups / edited by Pierre-Emmanuel Caprace, Université Catholique de Louvain, Belgium ; Nicolas Monod, École Polytechnique Fédérale de Lausanne. |
| title_short | New directions in locally compact groups / |
| title_sort | new directions in locally compact groups |
| topic | Compact groups. http://id.loc.gov/authorities/subjects/sh85029280 Groupes compacts. MATHEMATICS Algebra Intermediate. bisacsh Grupos compactos embucm Compact groups fast |
| topic_facet | Compact groups. Groupes compacts. MATHEMATICS Algebra Intermediate. Grupos compactos Compact groups |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1694346 |
| work_keys_str_mv | AT capracepierreemmanuel newdirectionsinlocallycompactgroups AT monodnicolas newdirectionsinlocallycompactgroups |