Rapport sur la théorie classique des nœuds (2ème partie)

André Gramain

Séminaire Bourbaki (1990-1991)

  • Volume: 33, page 89-113
  • ISSN: 0303-1179

How to cite

top

Gramain, André. "Rapport sur la théorie classique des nœuds (2ème partie)." Séminaire Bourbaki 33 (1990-1991): 89-113. <http://eudml.org/doc/110150>.

@article{Gramain1990-1991,
author = {Gramain, André},
journal = {Séminaire Bourbaki},
keywords = {classification; knots with homeomorphic complements; indecomposable knots with isomorphic groups; existence of an essential annulus; uniqueness of factorization},
language = {fre},
pages = {89-113},
publisher = {Société Mathématique de France},
title = {Rapport sur la théorie classique des nœuds (2ème partie)},
url = {http://eudml.org/doc/110150},
volume = {33},
year = {1990-1991},
}

TY - JOUR
AU - Gramain, André
TI - Rapport sur la théorie classique des nœuds (2ème partie)
JO - Séminaire Bourbaki
PY - 1990-1991
PB - Société Mathématique de France
VL - 33
SP - 89
EP - 113
LA - fre
KW - classification; knots with homeomorphic complements; indecomposable knots with isomorphic groups; existence of an essential annulus; uniqueness of factorization
UR - http://eudml.org/doc/110150
ER -

References

top
  1. [A] J.W. Alexander - On the subdivision of a 3-space by a polyhedron, Proc. Nat. Acad. Sci. USA, 10 (1924), 8-10. JFM50.0659.01
  2. [BZ] G. Burde, H. Zieschang - Eine Kennzeichnung der Torusknoten, Math. Annalen, 167 (1966), 169-176. Zbl0145.20502MR210113
  3. - Knots, Walter de Gruyter, BerlinNew-York (1985). Zbl0568.57001
  4. [CF] J.W. Cannon, C.D. Feustel - Essential embeddings of annuli and Möbius bands in 3-manifolds, Trans. AMS, 215 (1976), 219-239. Zbl0314.55004MR391094
  5. [CGLS] M. Culler, C. Mc A. Gordon, J. Luecke, P.B. Shalen - Dehn surgery on knots, Ann. of Math.,125 (1987), 237-300. Zbl0633.57006MR881270
  6. [F] C.D. Feustel - On the torus theorem and its applications, Trans. AMS, 217 (1976), 1-43. Zbl0321.55006MR394666
  7. [FW] C.D. Feustel, W. Whitten - Groups and complements of knots, Can. J. of Math., 30 (1978), 1284-1295. Zbl0373.55003MR511562
  8. [Ga] D. Gabai - Foliations and the topology of 3-manifolds, III, J. Diff. Geom., 18 (1987), 479-536. Zbl0639.57008MR910018
  9. [GL] C. Mc A. Gordon, J. Luecke - Knots are determined by their complements, Journal of AMS, 2 (1989), 371-415. Zbl0678.57005MR965210
  10. [Gr] A. Gramain - Rapport sur la théorie classique des nœuds (1ère partie), Sém. Bourbaki, exposé n° 485, 1975-76, Lect. Notes in Math. n° 567, Springer (1977), 222-237. Zbl0342.57009
  11. [H] J. Hempel - 3-manifolds, Ann. of Math. Studies n° 86 (1976), Princeton Univ. Press. Zbl0345.57001MR415619
  12. [Ja] W. Jaco - Lectures on Three-Manifolds Theory, Reg. Conf. in Math. n° 43, AMS (1980). Zbl0433.57001MR565450
  13. [Jo] K. Johannson - Homotopy equivalence of 3-manifolds with boundaries, Lect. Notes in Math. n° 761, Springer (1979). Zbl0412.57007MR551744
  14. [F] F. Laudenbach - Topologie de la Dimension 3, Astérisque n° 12, S.M.F., Paris (1974). Zbl0293.57004
  15. [M] E.E. Moïse - Geometric Topology in Dimensions 2 and 3, Graduate Texts in Math.47, Springer (1977). Zbl0349.57001MR488059
  16. [N] D. Noga - Über den Aussenraum von Produktknoten und die Bedeutung der Fixgruppen, Math. Zeit., 101 (1967), 131-141. Zbl0183.52102MR219054
  17. [P] C. Papakyriakopoulos - On Dehn's lemma and the asphericity of knots, Ann. of Math., 66 (1957), 1-26. Zbl0078.16402MR90053
  18. [Scha] M. Scharlemann - Smooth spheres in R4 with four critical points are standard, Invent. Math., 70 (1985), 125-141. Zbl0559.57019MR774532
  19. [Schu] H. Schubert - Knoten und Vollringe, Acta Mat., 90 (1953), 131- 286. Zbl0051.40403MR72482
  20. [Sc] P. Scott - A new proof of the annulus and torus theorem, Amer. J. of Math., 102 (1980), 241-277. Zbl0439.57004MR564473
  21. [Si] J. Simon - An algebraic classification of knots in S3, Ann. of Math., 97 (1973), 1-13. Zbl0256.55003MR310861
  22. [ST] J. Stallings - On fibering certain 3-manifolds, in Topology of 3- manifolds and related topics (Proceedings of the 1961 Topology Conference, Univ. of Georgia), Prentice-Hall (1962). MR158375
  23. [Wa] F. Waldhausen - Gruppen mit Zentrum und 3-dimensionale Mannigfaltigkeiten, Topology6 (1967), 505-517. Zbl0172.48704MR236930
  24. - On irreducible 3-manifolds which are sufficiently large, Ann. of Math., 87 (1968), 56-88. Zbl0157.30603MR224099
  25. [Wh] W. Whitten - Algebraic and geometric characterizations of knots, Invent. Math., 26 (1974), 259-270. Zbl0291.55004MR365548
  26. - Knots complements and groups, Topology, 26 (1987), 41-44. Zbl0607.57004MR880506

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.