6 papers · 1 filter
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…
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…
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…