Results 11 to 20 of about 348 (37)

The Asymptotic Cone of Teichmuller Space: Thickness and Divergence [PDF]

, 2012
We study the asymptotic geometry of Teichmuller space equipped with the Weil‐ Petersson metric. In particular, we provide a characterization of the canonical finest pieces in the tree-graded structure of the asymptotic cone of Teichmuller space along the
H. Sultan
semanticscholar   +1 more source

Asymptotic cones of HNN extensions and amalgamated products [PDF]

, 2012
Gromov asked whether an asymptotic cone of a finitely generated group was always simply connected or had uncountable fundamental group. We prove that Gromov’s dichotomy holds for asymptotic cones with cut points, as well as HNN extensions and amalgamated
Curtis Kent
semanticscholar   +1 more source

The Threshold for Subgroup Profiles to Agree is Logarithmic

Theory of Computing, 2019
For primes p > 2 and e > 3 there are at least pe−3/e groups of order p2e+2 that have equal multisets of isomorphism types of proper subgroups and proper quotient groups, isomorphic character tables, and power maps.
James B. Wilson
semanticscholar   +1 more source

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

Local topological properties of asymptotic cones of groups [PDF]

, 2012
We define a local analogue to Gromov’s loop division property which we use to give a sufficient condition for an asymptotic cone of a complete geodesic metric space to have uncountable fundamental group. When considering groups our condition allows us to
G. Conner, Curtis Kent
semanticscholar   +1 more source

Commensurated subgroups, semistability and simple connectivity at infinity [PDF]

, 2012
A subgroup Q of a group G is commensurated if the commensurator of Q in G is the entire group G . Our main result is that a finitely generated group G containing an infinite, finitely generated, commensurated subgroup H of infinite index in G is one ...
Gregory R. Conner, M. Mihalik
semanticscholar   +1 more source

Amenability versus non‐exactness 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

Thompson’s group T has quadratic Dehn function

Forum of Mathematics, Sigma
We prove that Thompson’s group T and, more generally, all the Higman–Thompson groups $T_n$ have quadratic Dehn function.
Matteo Migliorini
doaj   +1 more source