3 papers
math.GR2026
Common overlattices in trees and trees with fins
Sam Shepherd
Bass and Kulkarni proved that any pair of free uniform lattices in the automorphism group of a tree have conjugates that both lie inside a third uniform lattice (which is not neces…
math.GR2025
Graphically discrete groups and rigidity
Alex Margolis, Sam Shepherd, Emily Stark +1
We introduce the notion of graphical discreteness to group theory. A finitely generated group is graphically discrete if whenever it acts geometrically on a locally finite graph, t…
math.GR2025
Splittings of One-Ended Groups with One-Ended Halfspaces
Michael Mihalik, Sam Shepherd
We introduce the notion of halfspaces associated to a group splitting, and investigate the relationship between the coarse geometry of the halfspaces and the coarse geometry of the…