13 citations · 31 across the 11 of their papers we have counts for
12 papers
Computations of parabolic character schemes of knots
Yunhi Cho, Hyuk Kim, Seonhwa Kim +1
We compute parabolic -character schemes of knots using the parabolic quandle. To this end, we introduce sign-refined arc-colorings and show that their si…
Rigidity of nonconvex polyhedra with respect to edge lengths and dihedral angles
Yunhi Cho, Seonhwa Kim
We prove that every three-dimensional polyhedron is uniquely determined by its dihedral angles and edge lengths, even if nonconvex or self-intersecting, under two plausible suffici…
Parabolic representations and generalized Riley polynomials
Yunhi Cho, Hyuk Kim, Seonhwa Kim +1
We generalize R. Riley's study about parabolic representations of two bridge knot groups to the general knots in . We utilize the parabolic quandle method for general knot dia…
Adjoint Reidemeister torsions from wrapped M5-branes
Dongmin Gang, Seonhwa Kim, Seokbeom Yoon
We introduce a vanishing property of adjoint Reidemeister torsions of a cusped hyperbolic 3-manifold derived from the physics of wrapped M5-branes on the manifold. To support our p…
Octahedral developing of knot complement II: Ptolemy coordinates and applications
Hyuk Kim, Seonhwa Kim, Seokbeom Yoon
It is known that a knot complement (minus two points) decomposes into ideal octahedra with respect to a given knot diagram. In this paper, we study the Ptolemy variety for such an…
Formality of Floer complex of the ideal boundary of hyperbolic knot complement
Youngjin Bae, Seonhwa Kim, Yong-Geun Oh
This is a sequel to the authors' article [BKO](arXiv:1901.02239). We consider a hyperbolic knot in a closed 3-manifold and the cotangent bundle of its complement $M \setmin…
A wrapped Fukaya category of knot complement
Youngjin Bae, Seonhwa Kim, Yong-Geun Oh
This is the first of a series of two articles where we construct a version of wrapped Fukaya category of the cotangent bundle $T^*(M \s…
Octahedral developing of knot complement I: pseudo-hyperbolic structure
Hyuk Kim, Seonhwa Kim, Seokbeom Yoon
It is known that a knot complement can be decomposed into ideal octahedra along a knot diagram. A solution to the gluing equations applied to this decomposition gives a pseudo-deve…
A classification of polyhedral graph by combinatorially rigid vertices
Seonhwa Kim, Yunhi Cho
When the number of non-triangular faces adjacent to a vertex is less than or equal to three, the vertex will be called (\emph{combinatorially}) \emph{rigid}. We study the n…
Volume of Hypercubes Clipped by Hyperplanes and Combinatorial Identities
Yunhi Cho, Seonhwa Kim
There is an elegant expression for the volume of hypercube clipped by a single hyperplane. In the article the formula is generalized to the case of more than one hyperpla…
Legendrian singular links and singular connected sums
Byung Hee An, Youngjin Bae, Seonhwa Kim
We study Legendrian singular links up to contact isotopy. Using a special property of the singular points, we define the singular connected sum of Legendrian singular links. This c…
Optimistic limits of Kashaev invariants and complex volumes of hyperbolic links
Jinseok Cho, Hyuk Kim, Seonhwa Kim
Yokota suggested an optimistic limit method of the Kashaev invariants of hyperbolic knots and showed it determines the complex volumes of the knots. His method is very effective an…