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Yu-Chan Chang

Publications and source records attributed to Yu-Chan Chang.

6 recordsLinked to original sources
arXiv2026

Matroids and isomorphism problems for Bestvina-Brady groups

We propose a factorization of the graph isomorphism problem for Bestvina-Brady groups (BBGs) through matroid theory. In particular, we show that finitely presented BBGs depend on their defining graphs only through their cycle matroids. On the other hand, we construct graphs of arbitrarily high connectivity such that they have non-isomorphic cycle matroids but their BBGs are isomorphic. To do so, we prove that if a graph admits a tree clique-spanner, then the Dicks-Leary presentation of its BBG can be explicitly simplified to a right-angled Artin group presentation. In particular, we show that BBGs defined by dually chordal graphs are right-angled Artin groups.

math.GR↗
arXiv2025

Complete classification of the Dehn functions of Bestvina-Brady groups

We prove that the Dehn function of every finitely presented Bestvina-Brady group grows as a linear, quadratic, cubic, or quartic polynomial. In fact, we provide explicit criteria on the defining graph to determine the degree of this polynomial. As a consequence, we identify an obstruction that prevents certain Bestvina-Brady groups from admitting a CAT(0) structure.

math.GR↗
arXiv2025

A graphical description of the BNS-invariants of Bestvina-Brady groups and the RAAG recognition problem

A finitely presented Bestvina-Brady group (BBG) admits a presentation involving only commutators. We show that if a graph admits a certain type of spanning trees, then the associated BBG is a right-angled Artin group (RAAG). As an application, we obtain that the class of BBGs contains the class of RAAGs. On the other hand, we provide a criterion to certify that certain finitely presented BBGs are not isomorphic to RAAGs (or more general Artin groups). This is based on a description of the Bieri-Neumann-Strebel invariants of finitely presented BBGs in terms of separating subgraphs, analogous to the case of RAAGs. As an application, we characterize when the BBG associated to a 2-dimensional flag complex is a RAAG in terms of certain subgraphs.

math.GR↗
arXiv2021

Identifying Dehn Functions of Bestvina--Brady Groups From Their Defining Graphs

Let $Γ$ be a finite simplicial graph such that the flag complex on $Γ$ is a $2$-dimensional triangulated disk. We show that with some assumptions, the Dehn function of the associated Bestvina--Brady group is either quadratic, cubic, or quartic. Furthermore, we can identify the Dehn function from the defining graph $Γ$.

math.GR↗