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
14 - L2-Betti number of discrete and non-discrete groups
Published online by Cambridge University Press: 05 February 2018
By
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. 205 - 226Publisher: Cambridge University PressPrint publication year: 2018
References
[1] . Elliptic operators, discrete groups and von Neumann algebras. In Colloque “Analyse et Topologie” en l'Honneur de Henri Cartan, Astérisque, No. 32–33, Soc. Math. France, Paris (1976), 43–72.
[2] and . Large scale homology theories and geometry. In Geometric topology, AMS/IP Stud. Adv. Math. Vol. 2 Amer. Math. Soc., Providence, RI (1997), 522–569.
[3] and . Filling-invariants at infinity for manifolds of nonpositive curvature. Trans. Amer. Math. Soc., 350 (1998) no. 8, 3393–3405.
[4] . Cohomology of groups, volume 87 of Graduate Texts in Mathematics. Springer-Verlag, New York (1994).
[5] and . L2-cohomology and group cohomology. Topology, 25 (1986) no. 2, 189–215.
[6] and . Metric Geometry of Locally Compact Groups. EMS Tracts in Mathematics Vol. 25. European Mathematical Society, Zürich (2016).
[7] , , , and . Compactly supported cohomology of buildings. Comment. Math. Helv., 85 (2010) no. 3, 551–582.
[8] . Topics in geometric group theory. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL (2000).
[9] . Thin buildings. Geom. Topol., 10 (2006) 667–694.
[10] . von Neumann categories and extended L2-cohomology. K-Theory, 15 (1998) no. 4, 347–405.
[11] . Invariant percolation and harmonic Dirichlet functions. Geom. Funct. Anal., 15 (2005) no. 5 1004–1051.
[12] . Invariants L2 de relations d'équivalence et de groupes. Publ. Math. Inst. Hautes E'tudes Sci., 95 (2002) 93–150.
[13] . On orbit equivalence of measure preserving actions. In: Rigidity in dynamics and geometry, 167–186, Springer, Berlin (2002).
[14] . Cohomologie des groupes topologiques et des alg`ebres de Lie, volume 2 of Textes Math'ematiques. CEDIC, Paris (1980).
[15] , and . L2-Betti numbers of locally compact groups and their cross section equivalence relations. ArXiv e-prints 1302.6753 (2013).
[16] . Dimension theory of arbitrary modules over finite von Neumann algebras and L2-Betti numbers. I. Foundations. J. reine angew. Math., 495 (1998) 135–162.
[17] . L2-invariants: theory and applications to geometry and K-theory, volume 44 of Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag, Berlin (2002).
[18] . Survey on classifying spaces for families of subgroups. In Infinite groups: geometric, combinatorial and dynamical aspects, volume 248 of Progr. Math., page 269–322. Birkhäuser, Basel (2005).
[19] , , and . Group approximation in Cayley topology and coarse geometry, III: Geometric property (T). Algebr. Geom. Topol., 15 (2015) no. 2, 1067–1091.
[20] . Continuous bounded cohomology of locally compact groups, volume 1758 of Lecture Notes in Mathematics. Springer-Verlag, Berlin (2001).
[21] and . On rings of operators. Ann. of Math. (2), 37 (1936) no. 1, 116–229.
[22] . Cohomologie Lp: invariance sous quasiisometries. Preprint (1995).
[23] . C-algebras and their automorphism groups, volume 14 of London Mathematical Society Monographs. Academic Press, Inc., London-New York (1979).
[24] . L2-Betti numbers of locally compact groups. C. R. Math. Acad. Sci. Paris, 351 (2013) no. 9–10, 339–342.
[25] . L2-Betti Numbers of Locally Compact Groups. ArXiv eprints 1104.3294 (2011).
[26] , and . L2-Betti numbers of totally disconnected groups and their approximation by Betti numbers of lattices. ArXiv e-prints 1612.04559 (2016).
[27] and Andreas Thom Group cocycles and the ring of affiliated operators. Invent. Math., 185 (2011) no. 3, 561–592.
[28] . L2-Betti numbers of discrete measured groupoids. Internat. J. Algebra Comput., 15 (2005) no. 5–6, 1169–1188.
[29] and . Vanishing of 2-Betti numbers of locally compact groups as an invariant of coarse equivalence. ArXiv e-prints 1702.01685 (2017).
[30] . Metrics in locally compact groups. Compositio Math., 28 (1974), 217–222.
[31] . Theory of operator algebras. I, volume 124 of Encyclopaedia of Mathematical Sciences. Springer-Verlag, Berlin (2002).
[32] . Transformation groups, volume 8 of de Gruyter Studies in Mathematics. Walter de Gruyter & Co., Berlin (1987).