no. 2
Nœuds Fox-résiduellement nilpotents et rigidité virtuelle des variétés hyperboliques de dimension 3
Annales de l'Institut Fourier, Tome 48 (1998) no. 2, pp. 535-551.

En définissant une nouvelle classe de nœuds dans les variétés de dimension 3, on obtient une démonstration plus classique du théorème de rigidité virtuelle des variétés hyperboliques de D. Gabai.

We introduce a class of knots and use it to prove a topological rigidity criterion for homotopy equivalences between 3-manifolds. As an application, we give a new proof of Gabai’s virtual rigidity theorem for hyperbolic 3-manifolds.

@article{AIF_1998__48_2_535_0,
     author = {Dubois, Jo\"el},
     title = {N{\oe}uds {Fox-r\'esiduellement} nilpotents et rigidit\'e virtuelle des vari\'et\'es hyperboliques de dimension 3},
     journal = {Annales de l'Institut Fourier},
     pages = {535--551},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {48},
     number = {2},
     year = {1998},
     doi = {10.5802/aif.1628},
     mrnumber = {1625594},
     zbl = {0899.57008},
     language = {fr},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1628/}
}
TY  - JOUR
AU  - Dubois, Joël
TI  - Nœuds Fox-résiduellement nilpotents et rigidité virtuelle des variétés hyperboliques de dimension 3
JO  - Annales de l'Institut Fourier
PY  - 1998
SP  - 535
EP  - 551
VL  - 48
IS  - 2
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1628/
DO  - 10.5802/aif.1628
LA  - fr
ID  - AIF_1998__48_2_535_0
ER  - 
%0 Journal Article
%A Dubois, Joël
%T Nœuds Fox-résiduellement nilpotents et rigidité virtuelle des variétés hyperboliques de dimension 3
%J Annales de l'Institut Fourier
%D 1998
%P 535-551
%V 48
%N 2
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1628/
%R 10.5802/aif.1628
%G fr
%F AIF_1998__48_2_535_0
Dubois, Joël. Nœuds Fox-résiduellement nilpotents et rigidité virtuelle des variétés hyperboliques de dimension 3. Annales de l'Institut Fourier, Tome 48 (1998) no. 2, pp. 535-551. doi : 10.5802/aif.1628. https://aif.centre-mersenne.org/articles/10.5802/aif.1628/

[Du] J. Dubois, Nœuds géométriquement-libres et rigidité topologique des variétés de dimension 3, Thèse, Université Toulouse-III, 1996.

[Ep] D.B.A. Epstein, The degree of map, Proc. London Math. Soc., (3) 16 (1966), 369-383. | MR | Zbl

[Ga1] D. Gabai, Homotopy hyperbolic 3-manifolds are virtually hyperbolic, J. Amer. Math. Soc., 7 (1994), 193-198. | MR | Zbl

[Ga2] D. Gabai, Foliations and the topology of 3-manifolds, J. Differential Geom., 18 (1983), 445-503. | MR | Zbl

[GMT] D. Gabai, G.R. Meyerhoff, N. Thurston, Homotopy Hyperbolic 3-manifolds are hyperbolic, preprint. | MR | Zbl

[He] J. Hempel, 3-Manifolds, Ann. of Math. Stud., vol 86, Princeton Univ. Press, Princeton NJ, 1976. | MR | Zbl

[Hi] M.W. Hirsch, Differential topology, Springer-Verlag, Berlin-Heidelberg-New York, 1976. | MR | Zbl

[HS] J. Hass, P. Scott, Homotopy equivalence and homeomorphism of 3-manifolds, Topology, 31 (1992), 493-517. | MR | Zbl

[Ja] W. Jaco, Lecture on 3-manifold topology, CBMS Lecture Notes, No. 43, Amer. Math. Soc., Providence, RI, 1980. | MR | Zbl

[Jo] K. Johannson, Homotopy equivalences of 3-manifolds with boundaries, Lecture Note in Math. Vol. 761 (Springer, Berlin-Heidelberg-New York, 1979). | MR | Zbl

[JS] W. Jaco, P. Shalem, Seifert fibred spaces in 3-manifolds, Mem. Amer. Math. Soc., 220 (1980). | Zbl

[Kr] P.H. Kropholler, A note on centrality in 3-manifold groups, School of Math. Sci., Queen Mary College, London E1 4NS (1989), 261-266.

[Ma] W. Magnus, Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring, Math. Ann., 111 (1935). | JFM | Zbl

[Ma1] A. Mal'Cev, On isomorphic matrix representations of infinite groups, Math. Sb., 8 (50) (1940), 405-422. | MR | Zbl

[Sa] T. Sakai, Geodesic knots in hyperbolic 3-manifold, Kobe J. Math., 8 (1991), 81-87. | MR | Zbl

[Sc1] P. Scott, The geometry of 3-manifolds, Bull. London Math. Soc., 15 (1983), 401-487. | MR | Zbl

[Sc2] P. Scott, There are no fake Seifert fibred spaces with infinite π1, Ann. of Math., (2) 117 (1983), 35-70. | MR | Zbl

[St] J. Stallings, Homology and Central Series of Groups, J. Algebra, 2 (1965), 170-181. | MR | Zbl

[Th1] W. Thurston, Geometry and topology of 3-manifolds, Lecture Notes, Princeton University, Princeton NJ, 1978-1979.

[Th2] W. Thurston, Three dimensionnal manifolds, Kleinian groups, and hyperbolic geometry, Bull. Amer. Math. Soc., 6 (1982) 357-381. | Zbl

[Wa1] F. Waldhausen, On irreducible 3-manifolds which are sufficiently large, Ann. of Math., (2) 87 (1968), 56-88. | MR | Zbl

[Wa2] F. Waldhausen, On the determination of some bounded 3-manifold by their fundamental groups alone, Proc. of Int. Sym. of Topology, Hercy-Novi, Yugoslavia, 1968 : Beograd (1969), 331-332. | Zbl

[Wr] A.H. Wright, Monotone mappings and degree one mappings between pl manifolds, Geometry Topology (Proc. Conf., Park City, Utah, 1974), Lecture Note in Math. Vol 438, Springer, Berlin (1975) 441-459. | MR | Zbl

Cité par Sources :