26 citations · 115 across the 31 of their papers we have counts for
32 papers
Torsion of every finite order in the homology of graph braid groups
Byung Hee An
We determine the torsion subgroup of for and : top homology with arbitrary coefficients is the kernel of an unsigned…
Hierarchical geometry and right-angled Artin groups in graph braid groups
Byung Hee An, Sangrok Oh, Jihoon Park
For the unordered discrete configuration space of particles on a connected finite graph , we construct an explicit factor system on its univ…
Extending Goldberg's Exact Sequence to Braid Groups of Graphs and Simplicial Complexes
Byung Hee An
For a finite connected simplicial complex , the strand map , from to , sends a pure braid to the homotopy classes of its str…
Cubical structures and the large-scale geometry of graph braid groups
Byung Hee An, Sangrok Oh
We study the large-scale geometry of graph braid groups through the cubical structure of their unordered discrete configuration spaces, focusing on quasi-isometry to right-angled A…
Corrigendum to "Asymptotic homology of graph braid groups"
Byung Hee An, Gabriel C. Drummond-Cole, Ben Knudsen
We correct an error in the paper referred to in the title. Part of the argument is organized as a general method for establishing when (derived) functors factor through a fixed Ser…
On coshuffle comultiplication on configuration spaces
Byung Hee An
We introduce a coshuffle comultiplication on the singular chain complex of configuration spaces, and we show that this structure endows the configuration space with the structure o…
Hilbert polynomials of configuration spaces over graphs of circumference at most 1
Byung Hee An, Jang Soo Kim
The -configuration space of a topological space is the space of sets of distinct points in . In this paper, we consider the case where is a graph o…
Quasi-isometry classification of certain graph -braid groups and its applications
Byung Hee An, Sangrok Oh
In \cite{Oh22}, the second author defined a complex of groups decomposition of the fundamental group of a finitely generated 2-dimensional special group, called an \emph{intersecti…
The automorphism groups of Artin groups of edge-separated CLTTF graphs
Byung Hee An, Youngjin Cho
We provide an explicit presentation of the automorphism group of an edge-separated CLTTF Artin group.
Lagrangian fillings for Legendrian links of finite or affine Dynkin type
Byung Hee An, Youngjin Bae, Eunjeong Lee
We prove that there are at least as many exact embedded Lagrangian fillings as seeds for Legendrian links of finite type or affine type $\tilde{\mathsf{D}} \tilde{\m…
Lagrangian fillings for Legendrian links of affine type
Byung Hee An, Youngjin Bae, Eunjeong Lee
We prove that there are at least as many exact embedded Lagrangian fillings as seeds for Legendrian links of affine type . We also provide as…
On folded cluster patterns of affine type
Byung Hee An, Eunjeong Lee
A cluster algebra is a commutative algebra whose structure is decided by a skew-symmetrizable matrix or a quiver. When a skew-symmetrizable matrix is invariant under an action of a…
Lagrangian fillings for Legendrian links of finite type
Byung Hee An, Youngjin Bae, Eunjeong Lee
We prove that there are at least seeds many exact embedded Lagrangian fillings for Legendrian links of type . We also provide seeds many Lagrangian fillings with cert…
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.
Augmentations are sheaves for Legendrian graphs
Byung Hee An, Youngjin Bae, Tao Su
In this article, associated to a (bordered) Legendrian graph, we study and show the equivalence between two categorical Legendrian isotopy invariants: the augmentation category, a…
Augmentations and ruling polynomials for Legendrian graphs
Byung Hee An, Youngjin Bae, Tao Su
In this article, associated to a (bordered) Legendrian graph, we study and show the equivalence between two Legendrian isotopy invariants: augmentation number via point-counting ov…
Ruling invariants for Legendrian graphs
Byung Hee An, Youngjin Bae, Tamás Kálmán
We define ruling invariants for even-valence Legendrian graphs in standard contact three-space. We prove that rulings exist if and only if the DGA of the graph, introduced by the f…
Edge stabilization in the homology of graph braid groups
Byung Hee An, Gabriel C. Drummond-Cole, Ben Knudsen
We introduce a novel type of stabilization map on the configuration spaces of a graph, which increases the number of particles occupying an edge. There is an induced action on homo…
A Chekanov-Eliashberg algebra for Legendrian graphs
Byung Hee An, Youngjin Bae
We define a differential graded algebra for Legendrian graphs and tangles in the standard contact Euclidean three space. This invariant is defined combinatorially by using ideas fr…
Grid diagram for singular links
Byung Hee An, Hwa Jeong Lee
In this paper, we define the set of singular grid diagrams which provides a unified description for singular links, singular Legendrian links, singular transverse li…
Subdivisional spaces and graph braid groups
Byung Hee An, Gabriel C. Drummond-Cole, Ben Knudsen
We study the problem of computing the homology of the configuration spaces of a finite cell complex . We proceed by viewing , together with its subdivisions, as a subdivision…