12 citations · 22 across the 10 of their papers we have counts for
12 papers
Coarse homological invariants of metric spaces
Alexander Margolis
Inspired by group cohomology, we define several coarse topological invariants of metric spaces. We define the coarse cohomological dimension of a metric space, and demonstrate that…
Quasi-isometric rigidity of extended admissible groups
Alex Margolis, Hoang Thanh Nguyen
We introduce the class of extended admissible groups, which include both fundamental groups of non-geometric 3-manifolds and Croke-Kleiner admissible groups. We show that the class…
Commensurated hyperbolic subgroups
Nir Lazarovich, Alex Margolis, Mahan Mj
We show that if H is a non-elementary hyperbolic commensurated subgroup of infinite index in a hyperbolic group G, then H is virtually a free product of hyperbolic surface groups a…
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…
Model geometries of finitely generated groups
Alex Margolis
We study model geometries of finitely generated groups. If a finitely generated group does not contain a non-trivial finite rank free abelian commensurated subgroup, we show any mo…
Discretisable quasi-actions I: Topological completions and hyperbolicity
Alex Margolis
We define and develop the notion of a discretisable quasi-action. It is shown that a cobounded quasi-action on a proper non-elementary hyperbolic space not fixing a point of $\…
Counting lattices in products of trees
Nir Lazarovich, Ivan Levcovitz, Alex Margolis
A BMW group of degree is a group that acts simply transitively on vertices of the product of two regular trees of degrees and . We show that the number of commensura…
Planar lattice subsets with minimal vertex boundary
Radhika Gupta, Ivan Levcovitz, Alexander Margolis +1
A subset of vertices of a graph is minimal if, within all subsets of the same size, its vertex boundary is minimal. We give a complete, geometric characterization of minimal sets f…
Groups of cohomological codimension one
Alexander Margolis
We show that if is an almost normal subgroup of such that both and are of type and vcd() = vcd() + 1, then is the fundamental group of a graph of gr…
The geometry of groups containing almost normal subgroups
Alexander Margolis
A subgroup is said to be almost normal if every conjugate of is commensurable to . If is almost normal, there is a well-defined quotient space . We show t…
Quasi-isometry classification of RAAGs that split over cyclic subgroups
Alexander Margolis
For a one-ended right-angled Artin group, we give an explicit description of its JSJ tree of cylinders over infinite cyclic subgroups in terms of its defining graph. This is then u…
Quasi-Isometry Invariance of Group Splittings over Coarse Poincaré Duality Groups
Alexander Margolis
We show that if is a group of type that is coarsely separated into three essential, coarse disjoint, coarse complementary components by a coarse $PD_n…