2 citations · 3 across the 11 of their papers we have counts for
12 papers
Cut pairs and Morse splitting of finitely generated groups
Suzhen Han, Hao Liang, Qing Liu
Bowditch's theorem for hyperbolic groups establishes a fundamental correspondence between splittings over two-ended subgroups and the existence of local cut points in the Gromov bo…
On Topology of Three-dimensional Continua with Singular Points
Hao Liang, Yunhao Qiu, Yan Tan +1
We propose to model the topology of three-dimensional (3D) continua by Yin sets, regular open semianalytic sets with bounded boundary. Our model differs from manifold-based models…
A Positivstellensatz on the Matrix Algebra of Finitely Generated Free Group
Hao Liang
Positivstellens{ä}tze are a group of theorems on the positivity of involution algebras over or . One of the most well-known Positivstellensatz is the solut…
Boundary rigidity of Gromov hyperbolic spaces
Hao Liang, Qingshan Zhou
We introduce the concept of boundary rigidity for Gromov hyperbolic spaces. We show that a proper geodesic Gromov hyperbolic space with a pole is boundary rigid if and only if its…
Homomorphisms to 3-manifold groups
Daniel Groves, Michael Hull, Hao Liang
We prove foundational results about the set of homomorphisms from a finitely generated group to the collection of all fundamental groups of compact 3-manifolds and answer questions…
Discrete representations of finitely generated groups into
Hao Liang
We prove a factorization theorem for Fuchsian groups similar to those proved by Agol and Liu for 3-manifold groups. As an application, we build Makanin-Razborov diagrams, which par…
On Seymour's Second Neighborhood Conjecture of m-free Digraphs
Hao Liang, Jun-Ming Xu
This paper gives an approximate result related to Seymour's Second Neighborhood conjecture, that is, for any -free digraph , there exists a vertex and a real numb…
Equations in nilpotent groups
Moon Duchin, Hao Liang, Michael Shapiro
We show that there exists an algorithm to decide any single equation in the Heisenberg group in finite time. The method works for all two-step nilpotent groups with rank-one commut…
Equation Problem over central extensions of hyperbolic groups
Hao Liang
The Equation Problem in finitely presented groups asks if there exists an algorithm which determines in finite amount of time whether any given equation system has a solution or no…
On the minimal feedback arc set of m-free Digraphs
Hao Liang, Jun-Ming Xu
For a simple digraph , let be the size of the smallest subset such that has no directed cycles, and let be the number of unordered pairs of…
A note on directed 4-cycles in digraphs
Hao Liang, Jun-Ming Xu
Using some combinatorial techniques, in this note, it is proved that if , then any digraph on vertices with minimum outdegree at least contains a directed c…
Centralizers of Finite Subgroups of the Mapping Class Group
Hao Liang
In this paper, we study the action of finite subgroups of the mapping class group of a surface on the curve complex. We prove that if the diameter of the almost fixed point set of…