3 papers
math.GT2025
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…
math.GT2024
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…
math.RT2024
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 solu…