26 citations · 115 across the 31 of their papers we have counts for
4 papers · 1 filter
On the second homology of planar graph braid groups
Byung Hee An, Ben Knudsen
We show that the second homology of the configuration spaces of a planar graph is generated under the operations of embedding, disjoint union, and edge stabilization by three atomi…
Universal properties of anyon braiding on one-dimensional wire networks
Tomasz Maciążek, Byung Hee An
We demonstrate that anyons on wire networks have fundamentally different braiding properties than anyons in 2D. Our analysis reveals an unexpectedly wide variety of possible non-ab…
Geometric presentations of braid groups for particles on a graph
Byung Hee An, Tomasz Maciazek
We study geometric presentations of braid groups for particles that are constrained to move on a graph, i.e. a network consisting of nodes and edges. Our proposed set of generators…
Asymptotic homology of graph braid groups
Byung Hee An, Gabriel C. Drummond-Cole, Ben Knudsen
We give explicit formulas for the asymptotic Betti numbers of the unordered configuration spaces of an arbitrary finite graph over an arbitrary field.