On the structure of the centralizer of a braid

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1. [1] Arnold V.I., The cohomology ring of the group of dyed braids, Mat. Zametki5 (1969) 227-231. Zbl0277.55002MR242196
2. [2] Benardete D., Gutierrez M., Nitecki Z., A combinatorial approach to reducibility of mapping classes, Contemporary Math.150 (1993) 1-31. Zbl0804.57005MR1234257
3. [3] Benardete D., Gutierrez M., Nitecki Z., Braids and the Nielsen–Thurston classification, J. Knot Theory Ramifications4 (1995) 549-618. Zbl0874.57010MR1361083
4. [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. Zbl1056.20023MR1922736
5. [5] Bestvina M., Haendel M., Train-tracks for surface homeomorphisms, Topology34 (1995) 109-140. Zbl0837.57010MR1308491
6. [6] Birman J., Braids, Links, and Mapping Class Groups, Annals of Math. Studies, vol. 82, Princeton University Press, 1975. Zbl0305.57013MR375281
7. [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. Zbl0937.20016MR1654165
8. [8] Birman J., Lubotzky A., McCarthy J., Abelian and solvable subgroups of the mapping class groups, Duke Math. J.50 (1983) 1107-1120. Zbl0551.57004MR726319
9. [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/. Zbl0982.57005MR1780208
10. [10] Burde G., Über Normalisatoren der Zopfgruppe, Abh. Math. Sem. Univ. Hamburg27 (1964) 97-115. Zbl0134.43104MR170954
11. [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. Zbl0852.57012MR1309126
12. [12] Eilenberg S., Sur les transformations périodiques de la surface de sphère, Fund. Math.22 (1934) 28-41. Zbl0008.37109
13. [13] El-Rifai E.A., Morton H.R., Algorithms for positive braids, Quart. J. Math. Oxford Ser. (2)45 (180) (1994) 479-497. Zbl0839.20051MR1315459
14. [14] Fathi A., Laudenbach F., Poenaru V., Travaux de Thurston sur les surfaces – séminaire Orsay, Astérisque, vols. 66–67, Société Math. de France, 1991. Zbl0406.00016MR1134426
15. [15] Fenn R., Rolfsen D., Zhu J., Centralisers in the braid group and singular braid monoid, Enseign. Math.42 (1996) 75-96. Zbl0869.20024MR1395042
16. [16] Franco N., González-Meneses J., Conjugacy problem for braid groups and Garside groups, J. Algebra266 (2003) 112-132. Zbl1043.20019MR1994532
17. [17] Franco N., González-Meneses J., Computation of centralizers in braid groups and Garside groups, Rev. Mat. Iberoamericana19 (2003) 367-384. Zbl1064.20040MR2023190
18. [18] Garside F.A., The braid group and other groups, Quart. J. Math. Oxford20 (1969) 235-254. Zbl0194.03303MR248801
19. [19] Gebhardt V., A new approach to the conjugacy problem in Garside groups, Preprint, math.GT/0306199. Zbl1105.20032MR2166805
20. [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. [21] Ivanov N.V., Subgroups of Teichmüller Modular Groups, Translations of Mathematical Monographs, vol. 115, AMS, 1992. Zbl0776.57001MR1195787
22. [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. [23] Ivanov N.V., Examples of centralizers in the Artin braid groups, Preprint, math.GT/0306418. 
24. [24] de Kerékjártó B., Über die periodischen Transformationen der Kreisscheibe und der Kugelfläche, Math. Annalen80 (1919) 3-7. JFM47.0526.05
25. [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. Zbl0788.58039MR1199073
26. [26] Makanin G.S., On normalizers in the braid group, Mat. Sb.86 (128) (1971) 171-179. Zbl0229.20035MR347988
27. [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. Zbl0965.20016MR1465028
28. [28] Orevkov S.Yu., Quasipositivity test via unitary representations of braid groups and its applications to real algebraic curves, J. Knot Theory Ramifications10 (7) (2001) 1005-1023. Zbl1030.20026MR1867106
29. [29] Paris L., Rolfsen D., Geometric subgroups of surface braid groups, Ann. Inst. Fourier49 (1999) 101-156. Zbl0962.20028MR1697370
30. [30] Penner R.C., Harer J.L., Combinatorics of Train Tracks, Annals of Math., vol. 125, Princeton University Press, Princeton, NJ, 1992. Zbl0765.57001MR1144770
31. [31] Sibert H., Extraction of roots in Garside groups, Comm. Algebra30 (6) (2002) 2915-2927. Zbl1007.20036MR1908246
32. [32] Styšnev V.B., Izv. Akad. Nauk SSSR Ser. Mat.42 (5) (1978) 1120-1131, 1183. MR513916
33. [33] Thurston W.P., On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. (N.S.)19 (1988) 417-431. Zbl0674.57008MR956596
34. [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. Zbl0764.20017MR1161694

1. Juan González-Meneses, Basic results on braid groups