5 citations · 17 across the 11 of their papers we have counts for
15 papers
Piecewise isometry groups of Euclidean tessellations
Robert Bieri, Alex Feingold, Daniel Studenmund
Given a tessellation of Euclidean or hyperbolic space, the piecewise isometry group is the group whose elements are given by cutting space into finitely many tessellated convex sub…
Counting flat cycles in the homology of locally symmetric spaces
Daniel Studenmund, Bena Tshishiku
Locally symmetric spaces like contain immersed compact flat manifolds of dimension equal to the real rank. We give a lower bound f…
Hall's universal group is a subgroup of the abstract commensurator of a free group
Edgar A. Bering, Daniel Studenmund
P. Hall constructed a universal countable locally finite group U, determined up to isomorphism by two properties: every finite group C is a subgroup of U, and every embedding of C…
Topological Models of Abstract Commensurators
Edgar A. Bering, Daniel Studenmund
The full solenoid over a topological space is the inverse limit of all finite covers. When is a compact Hausdorff space admitting a locally path connected universal cover,…
The dualizing module and top-dimensional cohomology group of
Andrew Putman, Daniel Studenmund
For a number ring , Borel and Serre proved that is a virtual duality group whose dualizing module is the Steinberg module. They also proved…
On abstract commensurators of surface groups
Khalid Bou-Rabee, Daniel Studenmund
Let be the fundamental group of a surface of finite type and Comm be its abstract commensurator. Then Comm contains the solvable Baumslag--Solitar groups $\langle a ,…
Commensurability growths of algebraic groups
Khalid Bou-Rabee, Tasho Kaletha, Daniel Studenmund
Fixing a subgroup in a group , the full commensurability growth function assigns to each the cardinality of the set of subgroups of with $[Γ: Γ\cap Δ][Δ: Γ\cap Δ…
Commensurability growth of branch groups
Khalid Bou-Rabee, Rachel Skipper, Daniel Studenmund
Fixing a subgroup in a group , the commensurability growth function assigns to each the cardinality of the set of subgroups of with $[Γ: Γ\cap Δ][Δ: Γ\cap Δ] = n…
Arithmetic lattices in unipotent algebraic groups
Khalid Bou-Rabee, Daniel Studenmund
Fixing an arithmetic lattice in an algebraic group , the commensurability growth function assigns to each the cardinality of the set of subgroups with $[Γ: Γ\cap Δ]…
Semidualities from products of trees
Daniel Studenmund, Kevin Wortman
Let be a global function field of characteristic , and let be a finite-index subgroup of an arithmetic group defined with respect to and such that any torsion elemen…
The topology of local commensurability graphs
Khalid Bou-Rabee, Daniel Studenmund
We initiate the study of the -local commensurability graph of a group, where is a prime. This graph has vertices consisting of all finite-index subgroups of a group, where a…
Full residual finiteness growths of nilpotent groups
Khalid Bou-Rabee, Daniel Studenmund
Full residual finiteness growth of a finitely generated group measures how efficiently word metric -balls of inject into finite quotients of . We initiate a study of…
Nonarchimedean superrigidity of solvable S-arithmetic groups
Dave Witte Morris, Daniel Studenmund
Let Gamma be an S-arithmetic subgroup of a solvable algebraic group G over an algebraic number field F, such that the finite set S contains at least one place that is nonarchimedea…
Commensurators of solvable S-arithmetic groups
Daniel Studenmund
We show that the abstract commensurator of an S-arithmetic subgroup of a solvable algebraic group over Q is isomorphic to the Q-points of an algebraic group, and compare this with…
Abstract commensurators of lattices in Lie groups
Daniel Studenmund
Let Gamma be a lattice in a simply-connected solvable Lie group. We construct a Q-defined algebraic group A such that the abstract commensurator of Gamma is isomorphic to A(Q) and…