Citation

BibTex format

@article{Costantino:2025:1751-8121/adb5de,
author = {Costantino, F and He, Y-H and Heyes, E and Hirst, E},
doi = {1751-8121/adb5de},
journal = {Journal of Physics A: Mathematical and Theoretical},
pages = {095201--095201},
title = {Learning 3-manifold triangulations},
url = {http://dx.doi.org/10.1088/1751-8121/adb5de},
volume = {58},
year = {2025}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - <jats:title>Abstract</jats:title>               <jats:p>Real 3-manifold triangulations can be uniquely represented by isomorphism signatures. Databases of these isomorphism signatures are generated for a variety of 3-manifolds and knot complements, using SnapPy and Regina, then these language-like inputs are used to train various machine learning architectures to differentiate the manifolds, as well as their Dehn surgeries, via their triangulations. Gradient saliency analysis then extracts key parts of this language-like encoding scheme from the trained models. The isomorphism signature databases are taken from the 3-manifolds’ Pachner graphs, which are also generated in bulk for some selected manifolds of focus and for the subset of the SnapPy orientable cusped census with <jats:inline-formula>                     <jats:tex-math/>                     <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll">                        <mml:mrow>                           <mml:mo><</mml:mo>                           <mml:mn>8</mml:mn>                        </mml:mrow>                     </mml:math>                  </jats:inline-formula> initial tetrahedra. These Pachner graphs are further analysed through the lens of network science to identify new structure in the triangulation representation; in particular for the hyperbolic case, a relation between the length of the shortest geodesic (systole) and the size of the Pachner graph’s ball is observed.</jats:p>
AU  - Costantino,F
AU  - He,Y-H
AU  - Heyes,E
AU  - Hirst,E
DO  - 1751-8121/adb5de
EP  - 095201
PY  - 2025///
SN  - 1751-8113
SP  - 095201
TI  - Learning 3-manifold triangulations
T2  - Journal of Physics A: Mathematical and Theoretical
UR  - http://dx.doi.org/10.1088/1751-8121/adb5de
UR  - https://doi.org/10.1088/1751-8121/adb5de
VL  - 58
ER  -
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