Book contents
- Frontmatter
- Contents
- Foreword
- 1 On the role of totally disconnected groups in the structure of locally compact groups
- 2 Locally compact groups as metric spaces
- 3 A short primer on profinite groups
- 4 Lectures on Lie groups over local fields
- 5 Abstract quotients of profinite groups, after Nikolov and Segal
- 6 Automorphism groups of trees: generalities and prescribed local actions
- 7 Simon Smith's construction of an uncountable family of simple, totally disconnected, locally compact groups
- 8 The Neretin groups
- 9 The scale function and tidy subgroups
- 10 Contraction groups and the scale
- 11 The Bader–Shalom normal subgroup theorem
- 12 Burger–Mozes’ simple lattices
- 13 A lecture on invariant random subgroups
- 14 L2-Betti number of discrete and non-discrete groups
- 15 Minimal normal closed subgroups in compactly generated tdlc groups
- 16 Elementary totally disconnected locally compact groups, after Wesolek
- 17 The structure lattice of a totally disconnected locally compact group
- 18 The centraliser lattice
- 19 On the quasi-isometric classification of locally compact groups
- 20 Future directions in locally compact groups: a tentative problem list
- Index
- References
19 - On the quasi-isometric classification of locally compact groups
Published online by Cambridge University Press: 05 February 2018
Book contents
- Frontmatter
- Contents
- Foreword
- 1 On the role of totally disconnected groups in the structure of locally compact groups
- 2 Locally compact groups as metric spaces
- 3 A short primer on profinite groups
- 4 Lectures on Lie groups over local fields
- 5 Abstract quotients of profinite groups, after Nikolov and Segal
- 6 Automorphism groups of trees: generalities and prescribed local actions
- 7 Simon Smith's construction of an uncountable family of simple, totally disconnected, locally compact groups
- 8 The Neretin groups
- 9 The scale function and tidy subgroups
- 10 Contraction groups and the scale
- 11 The Bader–Shalom normal subgroup theorem
- 12 Burger–Mozes’ simple lattices
- 13 A lecture on invariant random subgroups
- 14 L2-Betti number of discrete and non-discrete groups
- 15 Minimal normal closed subgroups in compactly generated tdlc groups
- 16 Elementary totally disconnected locally compact groups, after Wesolek
- 17 The structure lattice of a totally disconnected locally compact group
- 18 The centraliser lattice
- 19 On the quasi-isometric classification of locally compact groups
- 20 Future directions in locally compact groups: a tentative problem list
- Index
- References
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- New Directions in Locally Compact Groups , pp. 275 - 342Publisher: Cambridge University PressPrint publication year: 2018
References
[1] . Specker-Kompaktifizierungen von lokal kompakten topologischen Gruppen. (German) Math. Z. 135 (1973/74), 325–361.
[2] . On a problem of Freudenthal's. Comp. Math. 35(1977), no. 1, 39–47.
[3] . Characterizing maximal compact subgroups. Arch. Math.
98 (2012), no. 6, 555–560.
[4] and . Uniform tree lattices. J. Amer. Math. Soc.
3 (1990), 843–902.
[5] , and . Kazhdan's Property (T). New Math. Monographs 11, Cambridge Univ. Press, Cambridge, 2008.
[6] and . Elements of asymptotic geometry. European Math. Soc. 2007.
[7] , , and . Amenable hyperbolic groups. J. Eur. Math. Soc. (JEMS)
17 (2015), no. 11, 2903–2947.
[8] . Commability of groups quasi-isometric to trees. ArXiv math/1312.0278 (2013).
[9] . Orlicz spaces and the large scale geometry of Heintze groups. Math. Ann.
368 (2017), no. 1-2, 433–481.
[10] and . Convergence groups and Seifert fibered 3-manifolds. Inv. Math. 118 (1994), no. 1, 441–456.
[11] . Groups quasi-isometric to complex hyperbolic space. Trans. Amer. Math. Soc.
348 (1996), 1757–1770.
[12] . Dimension of asymptotic cones of Lie groups. Journal of Topology
1 (2008), 342–361.
[13] . Commability and focal locally compact groups. Indiana Univ. Math. J.
64(1) (2015), 115–150.
[14] and . Metric geometry of locally compact groups. EMS Tracts in Mathematics, 25. European Mathematical Society (EMS), Zürich, 2016.
[15] and . Contracting automorphisms and Lp-cohomology in degree one. Ark. Mat.
49 (2011), no. 2, 295–324.
[16] and . Groups acting on graphs. Cambridge University Press, Cambridge, 1989.
[17] . The accessibility of finitely presented groups. Inventiones Mathematicae
81 (1985), no. 3, 449–457.
[18] . An inaccessible group. Geometric group theory, Vol. 1 (Sussex, 1991), pp. 75–78, London Math. Soc. Lecture Note Ser., 181, Cambridge University Press, Cambridge, 1993.
[19] . Quasisymmetric maps of boundaries of amenable hyperbolic groups. Indiana Univ. Math. J.
63(2), (2014), 329–343.
[20] and . Problems on the geometry of finitely generated solvable groups. In “Crystallographic Groups and their Generalizations (Kortrijk, 1999)”, Cont. Math. 262, Amer. Math. Soc. (2000).
[21] and . A note on spaces of asymptotic dimension one. Algebr. Geom. Topol.
7 (2007), 1063–1070.
[22] . Convergence groups are Fuchsian groups, Ann. of Math.
136 (1992), no. 3, 447–510.
[23] and . Isometry groups of Riemannian solvmanifolds. Trans. Amer. Math. Soc.
307 (1988), no. 1, 245–269.
[24] . Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2. Journal of Algebra
309 (2007), 640–653.
[25] . Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, (1987), 75–263.
[26] . Theorie von Carnot-Carathéodory Metriken und ihren Anwendungen, Dissertation, Rheinische Friedrich-Wilhelms-Univ. Bonn, 1986. Bonner Mathematische Schriften 180, 1987.
[27] . On homogeneous manifolds of negative curvature, Math. Ann.
211 (1974), 23–34.
[28] . The structure of certain quasisymmetric groups. Mem. Amer. Math. Soc.
83 (1990), no. 422.
[29] . Ends of locally compact groups and their coset spaces. J. Australian Math. Soc. 17, 274–284.
[30] and . Boundaries of hyperbolic groups. In: Combinatorial and geometric group theory (New York, 2000/Hoboken, NJ, 2001), 39–93, Contemp. Math. 296, Amer. Math. Soc., Providence, RI, 2002.
[31] and . Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings. Publ. Math. IHES 86 (1997), no. 1, 115–197.
[32] and . Induced quasi-actions: A remark. Proc. Amer. Math. Soc.
137 (2009), 1561–1567.
[33] . Lectures on group of transformations. Tata Institute of Fundamental Research, 1965.
[34] and . Analogues of Cayley graphs for topological groups. Math. Z.
258 (2008), no. 3, 637–675.
[35] . On the structure of groups with polynomial growth. Math. Z.
195 (1987), 109–117.
[36] . Adjoint and trivial cohomologies of nilpotent complex Lie algebras of dimension ≤ 7. Int. J. Math. Math. Sci. 2008, Art. ID 805305, 12 pp.
[37] . Continuous bounded cohomology of locally compact groups, Lecture Notes in Mathematics, vol. 1758, Springer-Verlag, Berlin, 2001.
[38] and , Topological transformation groups, New York, Interscience Publishers, Inc., 1955.
[39] , and . Maximally symmetric trees. Geom. Dedicata
92(1) (2002), 195–233.
[40] , and . Quasi-actions on trees I. Bounded valence. Ann. of Math.
158 (2003), 115–164.
[41] , and . Quasi-actions on trees II: Finite depth Bass–Serre trees. Mem. Amer. Math. Soc.
214 (2011), no. 1008.
[42] . Self-adjoint groups. Ann. of Math.
62(1) (1955), 44–55.
[43] . Quasi-conformal mappings in n-space and the rigidity of the hyperbolic space forms. Publ. Math. IHES
34 (1968), 53–104.
[44] . Croissance des boules et des géodésiques fermées dans les nilvariétés. Ergodic Theory Dynam. Systems
3 (1983), no. 3, 415–445.
[45] . Dimension conforme et sph`ere à l'infini des variétés à courbure négative, Ann. Acad. Sci. Fenn. Ser. A I Math. 14 (1989), no. 2, 177–212.
[46] . Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un. Ann. of Math. (1989), 1–60.
[47] . Cohomologie
Lp en degré 1 des espaces homog`enes. Potential Anal. 27 (2007), 151–165.
[48] . Coarse cohomology and index theory on complete manifolds. Mem. Amer. Math. Soc. 104, 1993.
[49] . Homological invariants and quasi-isometry. Geom. Funct. Anal.
16(2) (2006), 476–515.
[50] , Arbres, amalgames, SL2. Astérisque 46, Soc. Math. France 1977.
[51] . Harmonic analysis, cohomology, and the large-scale geometry of amenable groups. Acta Math.
192 (2004), 119–185.
[52] and . A rigidity property of some negatively curved solvable Lie groups. Comment. Math. Helv.
87(4) (2012), 805–823.
[53] . Endenverbande von Raumen und Gruppen. Math. Ann.
122 (1950), 167–174.
[54] . On torsion free groups with infinitely many ends. Ann. of Math.
88 (1968) 312–334.
[55] . Large scale Sobolev inequalities on metric measure spaces and applications. Rev. Mat. Iberoam.
24 (2008), no. 3, 825–864.
[56] . Vanishing of the first reduced cohomology with values in a Lprepresentation. Ann. Inst. Fourier 59 no.
2 (2009), 851–876.
[57] and . Vertex-transitive graphs and accessibility. J. Combin. Theory, Ser. B 58 (1993), no. 2, 248–268.
[58] . On quasiconformal groups. Journal d'Analyse Mathématique
46 (1986), no. 1, 318–346.
[59] . Homeomorphic conjugates of Fuchsian groups. Journal für die reine und angewandte Mathematik (Crelles Journal)
391 (1988), 1–54.
[60] . Amenability, bi-Lipschitz equivalence, and the von Neumann conjecture. Duke Math. J.
99 (1999), no. 1, 93–112.
[61] . The large scale geometry of the higher Baumslag–Solitar groups. Geom. Funct. Anal.
11(6) (2001), 1327–1343.
[62] . Quasisymmetric maps on the boundary of a negatively curved solvable Lie group. Math. Ann. 353(3) (2012), 727–746.
[63] . Large scale geometry of negatively curved RnR. Geom. Topol.
18 (2014), 831–872.