Some non-amenable groups

Aditi Kar, Graham A. Niblo

Type: Article

Publication Date: 2011-12-12

Citations: 3

DOI: https://doi.org/10.5565/publmat_56112_09

Abstract

We generalise a result of R. Thomas to establish the non-vanishing of the first 2 Betti number for a class of finitely generated groups.

Locations

Publicacions Matemàtiques - View
arXiv (Cornell University) - View - PDF
Dipòsit Digital de Documents de la UAB (Universitat Autònoma de Barcelona) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Some non-amenable groups	2010	Aditi Kar Graham A. Niblo
+	Torsion homology growth and cheap rebuilding of inner-amenable groups	2024	Matthias Uschold
+	Torsion homology growth and cheap rebuilding of inner-amenable groups	2022	Matthias Uschold
+	On a problem of day on nonelementary amenable groups in the class of finitely defined groups	1996	Rostislav Grigorchuk
+	Amenable Groups	2023	Tullio Ceccherini‐Silberstein Michel Coornaert
+	Certain Subgroups of the Betti-Mathieu Group	1900	L. E. Dickson
+	Finite groups with few non-linear irreducible characters	1974	J. Pelikán
+	A refinement of bounded cohomology	2022	Światosław R. Gal Jarek Kędra
+	The Shannon-McMillan-Breiman theorem for a class of amenable groups	1983	Donald Ornstein Benjamin Weiss
+	Monotileable Amenable Groups: An Application	2021	Amal Mohammed Ahmed Gaweash Hayat Yousuf Ismail Bakur Mariam Almahdi Mohammed Mu’lla
+	On vanishing criteria of $L^2$-Betti numbers of groups	2023	Pablo Sánchez-Peralta
+ PDF Chat	Non-amenable groups with amenable action and some paradoxical decompositions in the plane	1998	Jan Mycielski
+	A short proof of the Approximation Conjecture for amenable groups	2008	Daniel Pape
+	$L^2$-Betti numbers and non-unitarizable groups without free subgroups	2008	D. Osin
+	Bounds in groups with trivial Frattini subgroup	2007	Zoltán Halasi Károly Podoski
+	Amenable Locally Compact Groups	1984	Jean-Paul Pier
+ PDF Chat	Groups with finitely many non-normal subgroups	1990	N.S. Hekster H. W. Lenstra
+ PDF Chat	Rank gradient and torsion groups	2010	D. Osin
+	Hereditarily just-infinite torsion groups with positive first $\ell^2$-Betti number	2024	Steffen Kionke Eduard Schesler
+	Finite groups with few non-normal subgroups	2015	邱燕燕卢家宽庞琳娜

Works That Cite This (3)

Action	Title	Year	Authors
+	The first $\ell^2$-Betti number and groups acting on trees.	2020	Indira Chatterji Sam Hughes Peter H. Kropholler
+ PDF Chat	The first -betti number and groups acting on trees	2021	Indira Chatterji Sam Hughes Peter H. Kropholler
+	Residual Deficiency	2013	Mariano Zeron-Medina Laris

Works Cited by This (7)

Action	Title	Year	Authors
+	Relative Property (T) and the Vanishing of the first $\ell^2$-Betti number	2009	Talia Fernós
+	Spotting infinite groups	1999	Daniel Allcock
+	Cayley graphs and group presentations	1988	Richard M. Thomas
+	L2-Cohomology and group cohomology	1986	Jeff Cheeger Mikhael Gromov
+ PDF Chat	Group cocycles and the ring of affiliated operators	2011	Jesse Peterson Andreas Thom
+ PDF Chat	Introduction to ℓ2-methods in topology: Reduced ℓ2-homology, harmonic chains, ℓ2-betti numbers	2000	Beno Eckmann
+	L2-Invariants: Theory and Applications to Geometry and K-Theory	2002	Wolfgang Lück