A Structural Reclassification of Thurston's Eight Geometries Through Knot Complements

This paper reinterprets Thurston’s eight geometries through knot complements, showing how reflection, closure, and chirality encode geometric phases. The framework reveals non‑commutative residues distinguishing Nil, Sol, and SL2R~ from commutative geometries. This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0) license.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-02
DOI
https://doi.org/10.5281/zenodo.23090052
Primary Topic
Geometric and Algebraic Topology
Type
article
Field-Weighted Citation Impact
0.00
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article

A Structural Reclassification of Thurston's Eight Geometries Through Knot Complements

Shin Tamaki
Zenodo (CERN European Organization for Nuclear Research)
Geometric and Algebraic Topology
article

A Structural Reclassification of Thurston's Eight Geometries Through Knot Complements

Shin Tamaki
article en

Abstract

This paper reinterprets Thurston’s eight geometries through knot complements, showing how reflection, closure, and chirality encode geometric phases. The framework reveals non‑commutative residues distinguishing Nil, Sol, and SL2R~ from commutative geometries. This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0) license.

Zenodo (CERN European Organization for Nuclear Research)
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Geometric and Algebraic Topology
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A Structural Reclassification of Thurston's Eight Geometries Through Knot Complements — Shin Tamaki · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS