34 citations · 97 across the 14 of their papers we have counts for
20 papers
Strongly Quasiconvex subgroups in graphs of groups
Hoang Thanh Nguyen, Hung Cong Tran
Given a graph of groups with certain conditions on vertex groups and acts acylindrically on its Bass-Serre tree . Let be a finitely…
Superexponential Dehn functions inside CAT(0) groups
Noel Brady, Hung Cong Tran
We construct 4-dimensional CAT(0) groups containing finitely presented subgroups whose Dehn functions are for integers and 6-dimensional CAT(0) grou…
Divergence of finitely presented subgroups of CAT(0) groups
Noel Brady, Hung Cong Tran
We construct families of groups containing finitely presented groups whose divergence functions are of the form for a dense set of exponents and $r…
Coarse Alexander duality for pairs and applications
G. Christopher Hruska, Emily Stark, Hung Cong Tran
For a group (of type ) acting properly on a coarse Poincaré duality space , Kapovich-Kleiner introduced a coarse version of Alexander duality between and its compleme…
Divergence of finitely presented groups
Noel Brady, Hung Cong Tran
We construct families of finitely presented groups exhibiting new divergence behavior; we obtain divergence functions of the form for a dense set of exponents $α\in [2,\infty…
Quasiconvexity in -manifold groups
Hoang Thanh Nguyen, Hung Cong Tran, Wenyuan Yang
In this paper, we study strongly quasiconvex subgroups in a finitely generated --manifold group . We prove that if is a compact, orientable --manifold that does n…
The local-to-global property for Morse quasi-geodesics
Jacob Russell, Davide Spriano, Hung Cong Tran
We show the mapping class group, CAT(0) groups, the fundamental groups of closed 3-manifolds, and certain relatively hyperbolic groups have a local-to-global property for Morse qua…
Convexity in hierarchically hyperbolic spaces
Jacob Russell, Davide Spriano, Hung Cong Tran
Hierarchically hyperbolic spaces (HHSs) are a large class of spaces that provide a unified framework for studying the mapping class group, right-angled Artin and Coxeter groups, an…
On the coarse geometry of certain right-angled Coxeter groups
Hoang Thanh Nguyen, Hung Cong Tran
Let be a connected, triangle-free, planar graph with at least five vertices that has no separating vertices or edges. If the graph is , we prove that the rig…
On the relative hyperbolicity and manifold structure of certain right-angled Coxeter groups
Matthew Haulmark, Hoang Thanh Nguyen, Hung Cong Tran
In this article, we study the manifold structure and the relatively hyperbolic structure of right-angled Coxeter groups with planar nerves. We then apply our results to the quasi-i…
On strongly quasiconvex subgroups
Hung Cong Tran
We develop a theory of \emph{strongly quasiconvex subgroups} of an arbitrary finitely generated group. Strong quasiconvexity generalizes quasiconvexity in hyperbolic groups and is…
Surface group amalgams that (don't) act on 3-manifolds
G. Christopher Hruska, Emily Stark, Hung Cong Tran
We determine which amalgamated products of surface groups identified over multiples of simple closed curves are not fundamental groups of 3-manifolds. We prove each surface amalgam…
Malnormality and join-free subgroups in right-angled Coxeter groups
Hung Cong Tran
In this paper, we prove that all finitely generated malnormal subgroups of one-ended right-angled Coxeter groups are strongly quasiconvex and they are in particular quasiconvex whe…
Strong quasiconvexity, stability, and lower relative divergence in right-angled Artin groups
Hung Cong Tran
Let be a simplicial, finite, connected graph such that does not decompose as a nontrivial join. We prove that two notions of strong quasiconvexity and stability are equival…
On distortion of normal subgroups
Hung Cong Tran
We examine distortion of finitely generated normal subgroups. We show a connection between subgroup distortion and group divergence. We suggest a method computing the distortion of…
Divergence spectra and Morse boundaries of relatively hyperbolic groups
Hung Cong Tran
We introduce a new quasi-isometry invariant, called the divergence spectrum, to study finitely generated groups. We compare the concept of divergence spectrum with the other classi…
Geometric embedding properties of Bestvina-Brady subgroups
Hung Cong Tran
We compute the relative divergence and the subgroup distortion of Bestvina-Brady subgroups. We also show that for each integer , there is a free subgroup of rank of so…
Divergence of Morse geodesics
Hung Cong Tran
Behrstock and Druţu raised a question about the existence of Morse geodesics in spaces with divergence function strictly greater than and strictly less than $r^{n+1}…
Relative divergence of finitely generated groups
Hung Cong Tran
We generalize the concept of divergence of finitely generated groups by introducing the upper and lower relative divergence of a finitely generated group with respect to a subgroup…
Relations between various boundaries of relatively hyperbolic groups
Hung Cong Tran
Suppose a group is relatively hyperbolic with respect to a collection $\PP$ of its subgroups and also acts properly, cocompactly on a $\CAT(0)$ (or --hyperbolic) space .…