On the structure of the centralizer of a braid
González-Meneses, Juan ; Wiest, Bert
Annales scientifiques de l'École Normale Supérieure, Tome 37 (2004), p. 729-757 / Harvested from Numdam
@article{ASENS_2004_4_37_5_729_0,
     author = {Gonz\'alez-Meneses, Juan and Wiest, Bert},
     title = {On the structure of the centralizer of a braid},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {37},
     year = {2004},
     pages = {729-757},
     doi = {10.1016/j.ansens.2004.04.002},
     mrnumber = {2103472},
     zbl = {1082.20024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_2004_4_37_5_729_0}
}
González-Meneses, Juan; Wiest, Bert. On the structure of the centralizer of a braid. Annales scientifiques de l'École Normale Supérieure, Tome 37 (2004) pp. 729-757. doi : 10.1016/j.ansens.2004.04.002. http://gdmltest.u-ga.fr/item/ASENS_2004_4_37_5_729_0/

[1] Arnold V.I., The cohomology ring of the group of dyed braids, Mat. Zametki 5 (1969) 227-231. | MR 242196 | Zbl 0277.55002

[2] Benardete D., Gutierrez M., Nitecki Z., A combinatorial approach to reducibility of mapping classes, Contemporary Math. 150 (1993) 1-31. | MR 1234257 | Zbl 0804.57005

[3] Benardete D., Gutierrez M., Nitecki Z., Braids and the Nielsen-Thurston classification, J. Knot Theory Ramifications 4 (1995) 549-618. | MR 1361083 | Zbl 0874.57010

[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 1922736 | Zbl 1056.20023

[5] Bestvina M., Haendel M., Train-tracks for surface homeomorphisms, Topology 34 (1995) 109-140. | MR 1308491 | Zbl 0837.57010

[6] Birman J., Braids, Links, and Mapping Class Groups, Annals of Math. Studies, vol. 82, Princeton University Press, 1975. | MR 375281 | Zbl 0305.57013

[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 1654165 | Zbl 0937.20016

[8] Birman J., Lubotzky A., Mccarthy J., Abelian and solvable subgroups of the mapping class groups, Duke Math. J. 50 (1983) 1107-1120. | MR 726319 | Zbl 0551.57004

[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 1780208 | Zbl 0982.57005

[10] Burde G., Über Normalisatoren der Zopfgruppe, Abh. Math. Sem. Univ. Hamburg 27 (1964) 97-115. | MR 170954 | Zbl 0134.43104

[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 1309126 | Zbl 0852.57012

[12] Eilenberg S., Sur les transformations périodiques de la surface de sphère, Fund. Math. 22 (1934) 28-41. | Zbl 0008.37109

[13] El-Rifai E.A., Morton H.R., Algorithms for positive braids, Quart. J. Math. Oxford Ser. (2) 45 (180) (1994) 479-497. | MR 1315459 | Zbl 0839.20051

[14] Fathi A., Laudenbach F., Poenaru V., Travaux de Thurston sur les surfaces - séminaire Orsay, Astérisque, vols. 66-67, Société Math. de France, 1991. | MR 1134426 | Zbl 0406.00016

[15] Fenn R., Rolfsen D., Zhu J., Centralisers in the braid group and singular braid monoid, Enseign. Math. 42 (1996) 75-96. | MR 1395042 | Zbl 0869.20024

[16] Franco N., González-Meneses J., Conjugacy problem for braid groups and Garside groups, J. Algebra 266 (2003) 112-132. | MR 1994532 | Zbl 1043.20019

[17] Franco N., González-Meneses J., Computation of centralizers in braid groups and Garside groups, Rev. Mat. Iberoamericana 19 (2003) 367-384. | MR 2023190 | Zbl 1064.20040

[18] Garside F.A., The braid group and other groups, Quart. J. Math. Oxford 20 (1969) 235-254. | MR 248801 | Zbl 0194.03303

[19] Gebhardt V., A new approach to the conjugacy problem in Garside groups, Preprint, math.GT/0306199. | MR 2166805

[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 1195787 | Zbl 0776.57001

[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 47.0526.05

[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 1199073 | Zbl 0788.58039

[26] Makanin G.S., On normalizers in the braid group, Mat. Sb. 86 (128) (1971) 171-179. | MR 347988 | Zbl 0229.20035

[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 1465028 | Zbl 0965.20016

[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 1867106 | Zbl 1030.20026

[29] Paris L., Rolfsen D., Geometric subgroups of surface braid groups, Ann. Inst. Fourier 49 (1999) 101-156. | Numdam | MR 1697370 | Zbl 0962.20028

[30] Penner R.C., Harer J.L., Combinatorics of Train Tracks, Annals of Math., vol. 125, Princeton University Press, Princeton, NJ, 1992. | MR 1144770 | Zbl 0765.57001

[31] Sibert H., Extraction of roots in Garside groups, Comm. Algebra 30 (6) (2002) 2915-2927. | MR 1908246 | Zbl 1007.20036

[32] Styšnev V.B., Izv. Akad. Nauk SSSR Ser. Mat. 42 (5) (1978) 1120-1131, 1183. | MR 513916

[33] Thurston W.P., On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. (N.S.) 19 (1988) 417-431. | MR 956596 | Zbl 0674.57008

[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 1161694 | Zbl 0764.20017