Planar trees, slalom curves and hyperbolic knots

Norbert A'Campo

Publications Mathématiques de l'IHÉS (1998)

  • Volume: 88, page 171-180
  • ISSN: 0073-8301

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A'Campo, Norbert. "Planar trees, slalom curves and hyperbolic knots." Publications Mathématiques de l'IHÉS 88 (1998): 171-180. <http://eudml.org/doc/104135>.

@article{ACampo1998,
author = {A'Campo, Norbert},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {hyperbolic knots; fibered knots; monodromy diffeomorphism; slalom knot; Dynkin diagram},
language = {eng},
pages = {171-180},
publisher = {Institut des Hautes Études Scientifiques},
title = {Planar trees, slalom curves and hyperbolic knots},
url = {http://eudml.org/doc/104135},
volume = {88},
year = {1998},
}

TY - JOUR
AU - A'Campo, Norbert
TI - Planar trees, slalom curves and hyperbolic knots
JO - Publications Mathématiques de l'IHÉS
PY - 1998
PB - Institut des Hautes Études Scientifiques
VL - 88
SP - 171
EP - 180
LA - eng
KW - hyperbolic knots; fibered knots; monodromy diffeomorphism; slalom knot; Dynkin diagram
UR - http://eudml.org/doc/104135
ER -

References

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  1. [AC1] Norbert A'CAMPO, Le Groupe de Monodromie du Déploiement des Singularités Isolées de Courbes Planes II, Actes du Congrès International des Mathématiciens, tome 1, 395-404, Vancouver, 1974. Zbl0352.14011
  2. [AC2] Norbert A'CAMPO, Sur les valeurs propres de la transformation de Coxeter, Invent. Math. 33 (1976), 1, 61-67. Zbl0406.20041MR54 #12925
  3. [AC3] Norbert A'CAMPO, Real deformations and complex topology of plane curve singularities, Annales de la Faculté des Sciences de Toulouse, 8 (1999), 1, 5-23. Zbl0962.32025MR2001d:32043a
  4. [AC4] Norbert A'CAMPO, Generic immersions of curves, knots, monodromy and gordian number, Publ. Math. IHES (1999), this volume, 151-169. Zbl0960.57007
  5. [B-H] M. BESTVINA, M. HANDEL, Train-tracks for surface homeomorphisms, Topology, 34 (1995), 1, 109-140. Zbl0837.57010MR96d:57014
  6. [B-Z] M. BOILEAU and B. ZIMMERMANN, Symmetries of nonelliptic Montesinos links, Math. Ann. 277 (1987), 563-584. Zbl0608.57010MR88h:57004
  7. [B-S] Francis BONAHON, Lawrence SIEBENMANN, Geometric splittings of knots and Conway's algebraic knots, preprint (1987), see [Ka], chap. 10. 
  8. [B] N. BOURBAKI, Groupes et algèbres de Lie, éléments de Mathématique, 34, Hermann, Paris, 1968. Zbl0186.33001
  9. [F] Albert FATHI, Démonstration d'un théorème de Penner sur la composition des twists de Dehn, Bull. de la Soc. Math. de France 120 (1992), 467-484. Zbl0779.57005
  10. [G] Marc GIUSTI, Classification des singularités isolées d'intersections complètes simples, C.R. Acad. Sci. Paris Sér. A-B. 284 (1977), 1, A167-A170. Zbl0346.32015
  11. [H] Mikami HIRASAWA, Private communication and forthcoming article, Tokyo 1999. 
  12. [Hu] James E. HUMPHREYS, Reflection groups and Coxeter groups, Cambridge Studies in Adv. Math. 29, Cambridge University Press 1990. Zbl0725.20028MR92h:20002
  13. [Ka] Akio KAWAUCHI, A survey of knot theory, Birkhauser, Basel 1996. Zbl0861.57001
  14. [Kaw] Tomomi KAWAMURA, The unknotting numbers of 10139 and 10152 are 4, Osaka J. Math. 35 (1998), 3, 539-546. Zbl0909.57003
  15. [L] Jérôme LOS, On the forcing relation for surface homeomorphisms, Publ. Math. IHES 85 (1997), 5-61. Zbl0902.58028MR98h:58151
  16. [O] Jean-Pierre OTAL, Le théorème d'hyperbolisation pour les variétés fibrées de dimension 3, Astérisque 235, Soc. Math. de France 1996. Zbl0855.57003
  17. [Oe] U. OERTEL, Closed incompressible surfaces in complements of star links, Pacific J. of Math. 111, 209-230. Zbl0549.57004MR85j:57008
  18. [P] R. C. PENNER, A construction of pseudo-Anosov homeomorphisms, Trans. of the American Math. Soc. 310 (1988), 179-197. Zbl0706.57008MR89k:57026
  19. [R] D. ROLFSEN, Knots and links, Math. Lect. Note Series, 7, Publish or Perish Inc, 1976. Zbl0339.55004MR58 #24236
  20. [S-W] Makoto SAKUMA and Jeffrey WEEKS, Examples of canonical decompositions of hyperbolic link complements, Jap. J. of Math. 21 (1995), 2, 393-439. Zbl0858.57021MR96j:57013
  21. [S-Wh] Dennis STANTON, Dennis WHITE, Constructive Combinatorics, Undergraduate Texts in Mathematics, Springer-Verlag New-York Inc. 1986. Zbl0595.05002
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  23. [T2] W. THURSTON, On the geometry and topology of three manifolds, Preprint, Princeton 1977. 

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