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Journals / International Electronic Journal of Geometry / 2022 / Cilt: 15 - Sayı: 2

All Dehn Fillings of the Whitehead Link Complement are Tetrahedron Manifolds

Alberto CAVİCCHİOLİ
Fulvia SPAGGİARİ
Pages
192–201
Publication Date
2022-10-31
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The proof is based on techniques of Combinatorial Group Theory, and geometric presentations of manifold fundamental groups.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we show that Dehn surgeries on the oriented components of the Whitehead link yield tetrahedron manifolds of Heegaard genus $\le 2$.
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Key Findings & Data:As a consequence, the eight homogeneous Thurston 3-geometries are realized by tetrahedron manifolds of Heegaard genus $\le 2$.
💡
Conclusion & Impact:The proof is based on techniques of Combinatorial Group Theory, and geometric presentations of manifold fundamental groups.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Tetrahedron manifold · Whitehead link · Dehn surgery

Abstract

In this paper we show that Dehn surgeries on the oriented components of the Whitehead link yield tetrahedron manifolds of Heegaard genus $\le 2$. As a consequence, the eight homogeneous Thurston 3-geometries are realized by tetrahedron manifolds of Heegaard genus $\le 2$. The proof is based on techniques of Combinatorial Group Theory, and geometric presentations of manifold fundamental groups.

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Cite This Article

CAVİCCHİOLİ, A., SPAGGİARİ, F. (2022). All Dehn Fillings of the Whitehead Link Complement are Tetrahedron Manifolds. International Electronic Journal of Geometry, Cilt: 15 - Sayı: 2, 192–201. https://ajindex.com/articles/672029

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References (18)

  1. M. Aschenbrenner, S. Friedl and H. Wilton, Decision problems for 3-manifolds and their fundamental groups, Geometry & Topology Monographs 19 (2015), 201-236
  2. M. Brittenham and Y.Q. Wu, The classification of exceptional Dehnsurgeries on 2-bridge knots, Commun. Analysis Geom. 9 (1) (2001),97-113
  3. A. Cavicchioli, E. Molnár and F. Spaggiari, Some tetrahedron manifolds with Sol geometry and related groups, Journal of Geometry 105 (2014), 601-614
  4. A. Cavicchioli and F. Spaggiari, Tetrahedron manifold series of Heegaard genus two with knot presentation and Dehn surgery, Acta Math. Hungarica 131 (4) (2011), 307-322
  5. A. Cavicchioli, F. Spaggiari and A.I. Telloni, Topology of compact space forms from Platonic solids I, Topology and its Appl. 156 (2009), 812- 822
  6. A. Cavicchioli, F. Spaggiari and A.I. Telloni, Dehn surgeries on some classical links, Proceed. Edinburgh Math. Soc. 54 (2011), 33-45
  7. A.W.M. Dress, D.H. Huson and E. Molnár, The classification of face-transitive periodic three-dimensional tilings, Acta Crystallogr. A 49(1993), 806-817
  8. D.L. Johnson, Presentations of Groups, London Math. Soc. Stud. Texts, vol. 15, Cambridge Univ. Press, Cambridge, 1990
  9. R.C. Lyndon and P.E. Schupp, Combinatorial Group Theory, Springer- Verlag, Berlin-Heidelberg-New York, 1976
  10. B. Martelli and C. Petronio, Dehn Filling of the "magic " 3-manifold, Commun. in Analysis and Geom. 14 (5) (2006), 969-1026
  11. A.D. Mednykh and A. Yu. Vesnin, On Heegaard genus of three-dimensional hyperbolic manifolds of small volume, Sb. Math. J. 37 (5) (1996), 893- 897
  12. A.D. Mednykh and A. Yu. Vesnin, Covering properties of small volume hyperbolic 3-manifolds, J. Knot Theory Ram. 7 (3) (1998), 381-392
  13. E. Molnár, Tetrahedron manifolds and space forms, Note Mat. 10 (1990), 335-346
  14. E. Molnár, Polyhedron complexes with simply transitive group actions and their realizations, Acta Math. Hung. 59 (1-2) (1992), 175-216
  15. E. Molnár, On non-Euclidean crystallography, some football manifolds, Structural Chemistry 23 (2012), 1057-1069
  16. E. Molnár and J. Szirmai, Symmetries in the 8 homogeneous 3-geometries, Symmetry: Culture and Science 21 (1-3) (2010), 87-117
  17. E. Molnár and J. Szirmai, Hyperbolic space forms with crystallographic applications and visualizations, In: International Conference on Geom- etry and Graphics, Springer Verlag, Cham (2018), pp. 320-337
  18. J. M. Montesinos, Classical Tesselations and Three-Manifolds, Universite