Results 1 to 10 of about 314 (23)
Density of Metric Small Cancellation in Finitely Presented Groups [PDF]
Groups, Complexity, Cryptology, 2020 Small cancellation groups form an interesting class with many desirable properties. It is a well-known fact that small cancellation groups are generic; however, all previously known results of their genericity are asymptotic and provide no information ...
Alex Bishop, Michal Ferov
doaj +1 more source
Sub-Finsler Horofunction Boundaries of the Heisenberg Group
Analysis and Geometry in Metric Spaces, 2021 We give a complete analytic and geometric description of the horofunction boundary for polygonal sub-Finsler metrics, that is, those that arise as asymptotic cones of word metrics, on the Heisenberg group.
Fisher Nate, Golo Sebastiano Nicolussi
doaj +1 more source
Injectivity results for coarse homology theories
Proceedings of the London Mathematical Society, Volume 121, Issue 6, Page 1619-1684, December 2020., 2020 Abstract We show injectivity results for assembly maps using equivariant coarse homology theories with transfers. Our method is based on the descent principle and applies to a large class of linear groups or, more generally, groups with finite decomposition complexity.
Ulrich Bunke +3 more
wiley +1 more source
The Asymptotic Dimension of the First Grigorchuk Group is Infinity [PDF]
, 2006 We prove that the asymptotic dimension of the first Grigorchuk group is infinity.Comment: 3 ...
Smith, J.
core +4 more sources
Representation growth and representation zeta functions of groups [PDF]
, 2012 We give a short introduction to the subject of representation growth and representation zeta functions of groups, omitting all proofs. Our focus is on results which are relevant to the study of arithmetic groups in semisimple algebraic groups, such as ...
Klopsch, Benjamin
core +3 more sources
Amenability versus nonâexactness of dense subgroups of a compact group
Journal of the London Mathematical Society, Volume 100, Issue 2, Page 592-622, October 2019., 2019 Abstract Given a countable residually finite group, we construct a compact group K and two elements w and u of K with the following properties: The group generated by w and u3 is amenable, the group generated by w and u contains a copy of the given group, and these two groups are dense in K.
Masato Mimura
wiley +1 more source
Group Approximation in Cayley Topology and Coarse Geometry, Part II: Fibred Coarse Embeddings
Analysis and Geometry in Metric Spaces, 2019 The objective of this series is to study metric geometric properties of disjoint unions of Cayley graphs of amenable groups by group properties of the Cayley accumulation points in the space of marked groups.
Mimura Masato, Sako Hiroki
doaj +1 more source
A $p$-group with positive Rank Gradient [PDF]
, 2011 We construct for $d\geq 2$ and $\epsilon>0$ a $d$-generated $p$-group $\Gamma$, which in an asymptotic sense behaves almost like a $d$-generated free pro-$p$-group.
Schlage-Puchta, Jan-Christoph
core +1 more source
Isometric group actions on Hilbert spaces: growth of cocycles [PDF]
, 2005 We study growth of 1-cocycles of locally compact groups, with values in unitary representations. Discussing the existence of 1-cocycles with linear growth, we obtain the following alternative for a class of amenable groups G containing polycyclic groups ...
de Cornulier, Yves +2 more
core +5 more sources
Growth of quotients of groups acting by isometries on Gromov hyperbolic spaces [PDF]
, 2012 We show that every non-elementary group $G$ acting properly and cocompactly by isometries on a proper geodesic Gromov hyperbolic space $X$ is growth tight. In other words, the exponential growth rate of $G$ for the geometric (pseudo)-distance induced by $
Sabourau, Stephane
core +3 more sources