On the structure of the centralizer of a braid

González-Meneses, Juan; Wiest, Bert

doi:10.1016/j.ansens.2004.04.002

González-Meneses, Juan ; Wiest, Bert ¹

¹ Université de Rennes 1, Institut Mathématique, Campus de Beaulieu, 35042 Rennes Cedex (France)

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 37 (2004) no. 5, pp. 729-757.

MR Zbl | 2 citations dans Numdam

DOI : 10.1016/j.ansens.2004.04.002

Affiliations des auteurs :

González-Meneses, Juan ; Wiest, Bert ¹

¹ Université de Rennes 1, Institut Mathématique, Campus de Beaulieu, 35042 Rennes Cedex (France)

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González-Meneses, Juan; Wiest, Bert. On the structure of the centralizer of a braid. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 37 (2004) no. 5, pp. 729-757. doi : 10.1016/j.ansens.2004.04.002. http://www.numdam.org/articles/10.1016/j.ansens.2004.04.002/

Bibliographie
Cité par

[1] Arnold V.I., The cohomology ring of the group of dyed braids, Mat. Zametki 5 (1969) 227-231. | MR | Zbl

[2] Benardete D., Gutierrez M., Nitecki Z., A combinatorial approach to reducibility of mapping classes, Contemporary Math. 150 (1993) 1-31. | MR | Zbl

[3] Benardete D., Gutierrez M., Nitecki Z., Braids and the Nielsen-Thurston classification, J. Knot Theory Ramifications 4 (1995) 549-618. | MR | Zbl

[4] Bessis D., Digne F., Michel J., Springer theory in braid groups and the Birman-Ko-Lee monoid, Pacific J. Math. 205 (2) (2002) 287-309. | MR | Zbl

[5] Bestvina M., Haendel M., Train-tracks for surface homeomorphisms, Topology 34 (1995) 109-140. | MR | Zbl

[6] Birman J., Braids, Links, and Mapping Class Groups, Annals of Math. Studies, vol. 82, Princeton University Press, 1975. | MR | Zbl

[7] Birman J., Ko K.H., Lee S.J., A new approach to the word and conjugacy problems in the braid groups, Adv. Math. 139 (1998) 322-353. | MR | Zbl

[8] Birman J., Lubotzky A., Mccarthy J., Abelian and solvable subgroups of the mapping class groups, Duke Math. J. 50 (1983) 1107-1120. | MR | Zbl

[9] Brinkmann P., An implementation of the Bestvina-Handel algorithm for surface homeomorphisms, Experiment. Math. 9 (2000) 235-240, Computer program available at, http://www.math.uiuc.edu/~brinkman/software/train/. | MR | Zbl

[10] Burde G., Über Normalisatoren der Zopfgruppe, Abh. Math. Sem. Univ. Hamburg 27 (1964) 97-115. | MR | Zbl

[11] Constantin A., Kolev B., The theorem of Kerékjártó on periodic homeomorphisms of the disc and the sphere, Enseign. Math. (2) 40 (3-4) (1994) 193-204. | MR | Zbl

[12] Eilenberg S., Sur les transformations périodiques de la surface de sphère, Fund. Math. 22 (1934) 28-41. | Zbl

[13] El-Rifai E.A., Morton H.R., Algorithms for positive braids, Quart. J. Math. Oxford Ser. (2) 45 (180) (1994) 479-497. | MR | Zbl

[14] Fathi A., Laudenbach F., Poenaru V., Travaux de Thurston sur les surfaces - séminaire Orsay, Astérisque, vols. 66-67, Société Math. de France, 1991. | Numdam | MR | Zbl

[15] Fenn R., Rolfsen D., Zhu J., Centralisers in the braid group and singular braid monoid, Enseign. Math. 42 (1996) 75-96. | MR | Zbl

[16] Franco N., González-Meneses J., Conjugacy problem for braid groups and Garside groups, J. Algebra 266 (2003) 112-132. | MR | Zbl

[17] Franco N., González-Meneses J., Computation of centralizers in braid groups and Garside groups, Rev. Mat. Iberoamericana 19 (2003) 367-384. | MR | Zbl

[18] Garside F.A., The braid group and other groups, Quart. J. Math. Oxford 20 (1969) 235-254. | MR | Zbl

[19] Gebhardt V., A new approach to the conjugacy problem in Garside groups, Preprint, math.GT/0306199. | MR

[20] Hall T., Computer implementation of Bestvina-Handel algorithm, available at, http://www.liv.ac.uk/maths/PURE/MIN_SET/CONTENT/members/T_Hall.html.

[21] Ivanov N.V., Subgroups of Teichmüller Modular Groups, Translations of Mathematical Monographs, vol. 115, AMS, 1992. | MR | Zbl

[22] Ivanov N.V., Talk at the special session “Mapping class groups and the geometric theory of Teichmüller spaces” at the 974th meeting of the AMS, Ann Harbour, MI, March 1-3, 2002.

[23] Ivanov N.V., Examples of centralizers in the Artin braid groups, Preprint, math.GT/0306418.

[24] De Kerékjártó B., Über die periodischen Transformationen der Kreisscheibe und der Kugelfläche, Math. Annalen 80 (1919) 3-7. | JFM

[25] Los J., Pseudo-Anosov maps and invariant train tracks in the disc: a finite algorithm, Proc. London Math. Soc. (3) 66 (1993) 400-430. | MR | Zbl

[26] Makanin G.S., On normalizers in the braid group, Mat. Sb. 86 (128) (1971) 171-179. | MR | Zbl

[27] Manfredini S., Some subgroups of Artin's braid group. Special issue on braid groups and related topics (Jerusalem, 1995), Topology Appl. 78 (1-2) (1997) 123-142. | MR | Zbl

[28] Orevkov S.Yu., Quasipositivity test via unitary representations of braid groups and its applications to real algebraic curves, J. Knot Theory Ramifications 10 (7) (2001) 1005-1023. | MR | Zbl

[29] Paris L., Rolfsen D., Geometric subgroups of surface braid groups, Ann. Inst. Fourier 49 (1999) 101-156. | Numdam | MR | Zbl

[30] Penner R.C., Harer J.L., Combinatorics of Train Tracks, Annals of Math., vol. 125, Princeton University Press, Princeton, NJ, 1992. | MR | Zbl

[31] Sibert H., Extraction of roots in Garside groups, Comm. Algebra 30 (6) (2002) 2915-2927. | MR | Zbl

[32] Styšnev V.B., Izv. Akad. Nauk SSSR Ser. Mat. 42 (5) (1978) 1120-1131, 1183. | MR

[33] Thurston W.P., On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. (N.S.) 19 (1988) 417-431. | MR | Zbl

[34] Thurston W.P., Braid Groups, in: Epstein D.B.A., Cannon J.W., Holt D.F., Levy S.V.F., Paterson M.S., Thurston W.P. (Eds.), Word Processing in Groups, Jones and Bartlett Publishers, Boston, MA, 1992, Chapter 9. | MR | Zbl

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