The Profinite Completion of 3-Manifold Groups, Fiberedness and the Thurston Norm
| Autor: | Michel Boileau, Stefan Friedl |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Universität Regensburg (UR), I2m, Aigle, Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU) |
| Rok vydání: | 2020 |
| Předmět: |
Fibered knot
Figure-eight knot Group Theory (math.GR) 01 natural sciences Torus knot [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR] Combinatorics Mathematics - Geometric Topology [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] 0103 physical sciences FOS: Mathematics 0101 mathematics [MATH]Mathematics [math] Mathematics Trefoil knot [MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT] [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR] 010102 general mathematics Skein relation Geometric Topology (math.GT) Tricolorability 16. Peace & justice Mathematics::Geometric Topology Knot theory Algebra Knot invariant 010307 mathematical physics Mathematics - Group Theory |
| Zdroj: | What’s next? The mathematical legacy of William P. Thurston. What’s next? The mathematical legacy of William P. Thurston., 2020, ⟨10.1515/9780691185897⟩ |
| DOI: | 10.2307/j.ctvthhdvv.5 |
| Popis: | We show that a regular isomorphism of profinite completion of the fundamental groups of two 3-manifolds $N_1$ and $N_2$ induces an isometry of the Thurston norms and a bijection between the fibered classes. We study to what extent does the profinite completion of knot groups distinguish knots and show that it distinguishes each torus knot and the figure eight knot among all knots. We show also that it distinguishes between hyperbolic knots with cyclically commensurable complements under the assumption that their Alexander polynomials have at least one zero which is not a root of unity. 22 pages |
| Databáze: | OpenAIRE |
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