Un énoncé de Handel–Mosher certifie que le rapport des logarithmes des facteurs d'étirement d'un automorphisme iréductible du groupe libre et de son inverse est borné par une constante . Nous montrons dans la présente courte note que cette constante ne peut pas être choisie indépendante de N.
A result of Handel–Mosher guarantees that the ratio of logarithms of stretch factors of any fully irreducible automorphism of the free group and its inverse is bounded by a constant . In this short note, we show that this constant cannot be chosen independent of the rank N.
@article{CRMATH_2014__352_11_885_0, author = {Spencer Dowdall and Ilya Kapovich and Christopher J. Leininger}, title = {Unbounded asymmetry of stretch factors}, journal = {Comptes Rendus. Math\'ematique}, pages = {885--887}, publisher = {Elsevier}, volume = {352}, number = {11}, year = {2014}, doi = {10.1016/j.crma.2014.09.007}, language = {en}, }
Spencer Dowdall; Ilya Kapovich; Christopher J. Leininger. Unbounded asymmetry of stretch factors. Comptes Rendus. Mathématique, Volume 352 (2014) no. 11, pp. 885-887. doi : 10.1016/j.crma.2014.09.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.09.007/
[1] Asymmetry of outer space, Geom. Dedicata, Volume 156 (2012), pp. 81-92
[2] Train tracks and automorphisms of free groups, Ann. of Math. (2), Volume 135 (1992) no. 1, pp. 1-51
[3] A geometric invariant of discrete groups, Invent. Math., Volume 90 (1987) no. 3, pp. 451-477
[4] Dynamics on free-by-cyclic-groups, 2013 (preprint) | arXiv
[5] McMullen polynomials and Lipschitz flows for free-by-cyclic groups, 2013 (preprint) | arXiv
[6] The expansion factors of an outer automorphism and its inverse, Trans. Amer. Math. Soc., Volume 359 (2007) no. 7, pp. 3185-3208 (electronic)
[7] Parageometric outer automorphisms of free groups, Trans. Amer. Math. Soc., Volume 359 (2007) no. 7, pp. 3153-3183 (electronic)
Cité par Sources :
Commentaires - Politique