Author

B. An

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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

Extending Goldberg's Exact Sequence to Braid Groups of Graphs and Simplicial Complexes

For a finite connected simplicial complex $X$, the strand map $\iota_\ast$, from $\mathbb{P}_n(X)$ to $\prod_{i=1}^n\pi_1(X,x_i^0)$, sends a pure braid to the homotopy classes of its strands. A theorem of Goldberg (1973) computes its kernel when $X$ is a closed surface other than $S^2$ and $\mathbb{RP}^2$: the kernel i...

B. An · 0 citations