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.
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.
@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, Volume 48 (1998) no. 2, pp. 535-551. doi : 10.5802/aif.1628. https://aif.centre-mersenne.org/articles/10.5802/aif.1628/
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