Author

Sangrok Oh

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Preprint Sep 2026

Product subcomplexes and intersection complexes of weakly special square complexes

We define product subcomplexes and intersection complexes for compact nonpositively curved square complexes and CAT(0) square complexes. Product subcomplexes are defined as equivalence classes of local isometries from products of graphs with embedded coordinate fibers. Using their factorizations, we give a common defin...

Sang-Rok Oh · 1 citation

Preprint Sep 2026

Hierarchical geometry and right-angled Artin groups in graph braid groups

For the unordered discrete configuration space $\mathrm{UD}_n(\mathsf{\Gamma})$ of $n$ particles on a connected finite graph $\mathsf{\Gamma}$, we construct an explicit factor system on its universal cover. Its factors are encoded by legal pairs, namely subgraphs equipped with particle distributions. The nesting, ortho...

B. An, Sang-Rok Oh, JiHoon Park · 0 citations

Preprint Aug 2026

From algebraic orthogonality to RAAG embedding obstructions in hierarchically hyperbolic groups

We introduce the $\textit{expanded core graph}$, which records minimal unbounded domains and their axial directions, for two classes of hierarchically hyperbolic group structures modeled on compact special groups and mapping class groups. Our main structural result shows that every embedding of a right-angled Artin gro...

Sang-Rok Oh, JiHoon Park · 1 citation · ⚡1