13 citations · 47 across the 18 of their papers we have counts for
20 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…
1-loop equals torsion for two-bridge knots
Stavros Garoufalidis, Seokbeom Yoon
Motivated by the conjectured asymptotics of the Kashaev invariant, Dimofte and the first author introduced a power series associated to a suitable ideal triangulation of a cusped h…
The (twisted/)-Alexander polynomial of ideally triangulated 3-manifolds
Stavros Garoufalidis, Seokbeom Yoon
We establish a connection between the Alexander polynomial of a knot and its twisted and -versions with the triangulations that appear in 3-dimensional hyperbolic geometry. Sp…
1-loop equals torsion for fibered 3-manifolds
Nathan M. Dunfield, Stavros Garoufalidis, Seokbeom Yoon
In earlier work of two of the authors, two 1-loop polynomial invariants of cusped 3-manifolds were constructed using combinatorial data of ideal triangulations, and conjectured to…
Super-representations of 3-manifolds and torsion polynomials
Stavros Garoufalidis, Seokbeom Yoon
Torsion polynomials connect the genus of a hyperbolic knot (a topological invariant) with the discrete faithful representation (a geometric invariant). Using a new combinatorial st…
Asymptotically multiplicative quantum invariants
Stavros Garoufalidis, Seokbeom Yoon
The Euler characteristic and the volume are two best-known multiplicative invariants of manifolds under finite covers. On the other hand, quantum invariants of 3-manifolds are not…
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…
Twisted Neumann--Zagier matrices
Stavros Garoufalidis, Seokbeom Yoon
The Neumann--Zagier matrices of an ideal triangulation are integer matrices with symplectic properties whose entries encode the number of tetrahedra that wind around each edge of t…
The adjoint Reidemeister torsion for the connected sum of knots
Joan Porti, Seokbeom Yoon
Let be the connected sum of knots . It is known that the -character variety of the knot exterior of has a component of dimension…
Adjoint Reidemeister torsions of two-bridge knots
Seokbeom Yoon
We give an explicit formula for the adjoint Reidemeister torsion of two-bridge knots and prove that the adjoint Reidemeister torsion satisfies a certain type of vanishing identitie…
A vanishing identity on adjoint Reidemeister torsions of twist knots
Seokbeom Yoon
For a compact oriented 3-manifold with torus boundary the adjoint Reidemeister torsion is defined as a function on the -character variety depending on a…
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…
On the potential functions for a link diagram
Seokbeom Yoon
For an oriented diagram of a link in the 3-sphere, Cho and Murakami defined the potential function whose critical point, slightly different from the usual sense, corresponds to…
On the Hikami-Inoue conjecture
Jinseok Cho, Seokbeom Yoon, Christian K. Zickert
Given a braid presentation of a hyperbolic knot, Hikami and Inoue consider a system of polynomial equations arising from a sequence of cluster mutations determined by . They…
The volume and Chern-Simons invariant of a Dehn-filled manifold
Seokbeom Yoon
For a compact 3-manifold with non-empty boundary, Zickert gave a combinatorial formula for computing the volume and Chern-Simons invariant of a boundary parabolic representatio…
Partially abelian representations of knot groups
Yunhi Cho, Seokbeom Yoon
A knot complement admits a pseudo-hyperbolic structure by solving Thurston's gluing equations for an octahedral decomposition. It is known that a solution to these equations can be…
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…
Neukirch's Approach to the Reciprocity Map and Global Class Field theory in Positive Characteristic
Seok Ho Yoon
Neukirch developed an axiomatic and explicit approach to class field theory. This was applied to local fields and number fields but was never done for global function fields since…
Twisted Class Field Theory
Seok Ho Jack Yoon
Neukirch has developed explicit and axiomatic class field theory, which applies to both local and global fields. One of the key ingredients in his theory is a -ex…