This repository accompanies the paper
Mazur's Knot and the Octahedron
by Jack Calcut and Yangyang Du.
arXiv: https://arxiv.org/abs/2606.17335
It contains the complete source code for every computer calculation used in Sections 6–8 of the paper.
The file
00_Companion_Computations.pdf
contains the complete code, output, and a brief analysis for every computation. Together, this repository and the companion paper make all computations fully reproducible.
The computations require
- SageMath 10.7
- SnapPy 3.3.2
- GAP 4.14.0
00_Companion_Computations.pdf Companion paper containing the complete code, output, and analysis.
01_Mazur_knot_exterior.py Computes basic geometric information for the Mazur knot exterior.
02_Jester_knot_exterior.py Computes basic geometric information for the Jester knot exterior.
03_X_exceptional_fillings.py Distinguishes the exceptional fillings of the Mazur knot exterior.
04_systole_m137_t12072.py Computes the verified systoles of m137 and t12072.
05_compare_core_systole_m137.py Compares the filling core with the systole for fillings of m137.
06_compare_core_systole_t12072.py Compares the filling core with the systole for fillings of t12072.
07_drilled_manifolds_m137.py Computes the drilled manifolds for the remaining hyperbolic fillings of m137.
08_drilled_manifolds_t12072.py Computes the drilled manifolds for the remaining hyperbolic fillings of t12072.
09_systolic_geodesics_t12072_3_1_filled.py Verifies the two systolic geodesics of t12072(3,1).
10_compare_drilled.py Verifies that the drilled manifolds are pairwise nonisometric.
11_volume_filled_X.py Computes volumes of Dehn fillings of the Mazur knot exterior.
12_volume_filled_Y.py Computes volumes of Dehn fillings of the Jester knot exterior.
13_volume_symmetry_filled_Y.py Computes evidence for the Jester volume symmetry.
14_Whitehead_link_exterior_in_S3.py Computes basic information and cusp shapes of the Whitehead link exterior WS3 in S^3.
15_Whitehead_link_exterior_in_S1xS2.py Computes basic information and cusp shapes of the Whitehead link exterior W in S^1 × S^2.
If you use this code in research, then please cite
Jack Calcut and Yangyang Du, Mazur's Knot and the Octahedron, https://arxiv.org/abs/2606.17335
We will update this citation with the journal reference upon publication.
The code in this repository is released under the MIT License. See the file LICENSE for the complete license.
Questions, comments, and corrections are welcome.
Jack Calcut jcalcut@oberlin.edu
Yangyang Du yyadu@umich.edu