Volume 11, issue 5 (2011)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 6, 2415–2924
Issue 5, 1935–2414
Issue 4, 1463–1934
Issue 3, 963–1462
Issue 2, 509–962
Issue 1, 1–508

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Reducible braids and Garside Theory

Juan González-Meneses and Bert Wiest

Algebraic & Geometric Topology 11 (2011) 2971–3010
Bibliography
1 D Benardete, M Gutiérrez, Z Nitecki, A combinatorial approach to reducibility of mapping classes, from: "Mapping class groups and moduli spaces of Riemann surfaces (Göttingen, 1991/Seattle, WA, 1991)" (editors C F Bödigheimer, R M Hain), Contemp. Math. 150, Amer. Math. Soc. (1993) 1 MR1234257
2 M Bestvina, M Handel, Train-tracks for surface homeomorphisms, Topology 34 (1995) 109 MR1308491
3 J S Birman, V Gebhardt, J González-Meneses, Conjugacy in Garside groups I: Cyclings, powers and rigidity, Groups Geom. Dyn. 1 (2007) 221 MR2314045
4 J S Birman, V Gebhardt, J González-Meneses, Conjugacy in Garside groups II: Structure of the ultra summit set, Groups Geom. Dyn. 2 (2008) 13 MR2367207
5 J S Birman, A Lubotzky, J McCarthy, Abelian and solvable subgroups of the mapping class groups, Duke Math. J. 50 (1983) 1107 MR726319
6 M Calvez, B Wiest, Fast algorithmic Nielsen–Thurston classification of four-strand braids, to appear in J.Knot Theory Ramifications arXiv:1004.0067
7 A J Casson, S A Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Math. Soc. Student Texts 9, Cambridge Univ. Press (1988) MR964685
8 P Dehornoy, L Paris, Gaussian groups and Garside groups, two generalisations of Artin groups, Proc. London Math. Soc. $(3)$ 79 (1999) 569 MR1710165
9 E A El-Rifai, H R Morton, Algorithms for positive braids, Quart. J. Math. Oxford Ser. $(2)$ 45 (1994) 479 MR1315459
10 D B A Epstein, J W Cannon, D F Holt, S V F Levy, M S Paterson, W P Thurston, Word processing in groups, Jones and Bartlett (1992) MR1161694
11 B Farb, D Margalit, A primer on mapping class groups, Princeton Math. Ser. 49, Princeton Univ. Press (2011) 488
12 A Fathi, F Laudenbach, V Poénaru, editors, Travaux de Thurston sur les surfaces, Astérisque 66–67, Soc. Math. France (1979) 284 MR568308
13 N Franco, J González-Meneses, Conjugacy problem for braid groups and Garside groups, J. Algebra 266 (2003) 112 MR1994532
14 V Gebhardt, A new approach to the conjugacy problem in Garside groups, J. Algebra 292 (2005) 282 MR2166805
15 V Gebhardt, J González-Meneses, The cyclic sliding operation in Garside groups, Math. Z. 265 (2010) 85 MR2606950
16 V Gebhardt, J González-Meneses, Solving the conjugacy problem in Garside groups by cyclic sliding, J. Symbolic Comput. 45 (2010) 629 MR2639308
17 J González-Meneses, On reduction curves and Garside properties of braids, from: "Topology of algebraic varieties and singularities" (editors J I Cogolludo-Agustín, E Hironaka), Contemp. Math. 538, Amer. Math. Soc. (2011) 227 MR2777822
18 J González-Meneses, B Wiest, On the structure of the centralizer of a braid, Ann. Sci. École Norm. Sup. $(4)$ 37 (2004) 729 MR2103472
19 E K Lee, S J Lee, A Garside-theoretic approach to the reducibility problem in braid groups, J. Algebra 320 (2008) 783 MR2422316
20 E K Lee, S J Lee, Some power of an element in a Garside group is conjugate to a periodically geodesic element, Bull. Lond. Math. Soc. 40 (2008) 593 MR2438075
21 B Wiest, How to read the length of a braid from its curve diagram, Groups Geom. Dyn. 5 (2011) 673 MR2813531