Geometry & Topology Volume 15, issue 1 (2011)

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Braid ordering and the geometry of closed braid

Tetsuya Ito

Geometry & Topology 15 (2011) 473–498

DOI: 10.2140/gt.2011.15.473

Bibliography

1	J S Birman, E Finkelstein, Studying surfaces via closed braids, J. Knot Theory Ramifications 7 (1998) 267 MR1625362
2	J S Birman, M D Hirsch, A new algorithm for recognizing the unknot, Geom. Topol. 2 (1998) 175 MR1658024
3	J S Birman, K H Ko, S J Lee, A new approach to the word and conjugacy problems in the braid groups, Adv. Math. 139 (1998) 322 MR1654165
4	J S Birman, I Kofman, A new twist on Lorenz links, J. Topol. 2 (2009) 227 MR2529294
5	J S Birman, W W Menasco, Studying links via closed braids. IV. Composite links and split links, Invent. Math. 102 (1990) 115 MR1069243
6	J S Birman, W W Menasco, Studying links via closed braids. III. Classifying links which are closed $3$–braids, Pacific J. Math. 161 (1993) 25 MR1237139
7	J S Birman, W W Menasco, Special positions for essential tori in link complements, Topology 33 (1994) 525 MR1286930
8	J S Birman, W W Menasco, Stabilization in the braid groups. I. MTWS, Geom. Topol. 10 (2006) 413 MR2224463
9	P Dehornoy, Braid groups and left distributive operations, Trans. Amer. Math. Soc. 345 (1994) 115 MR1214782
10	P Dehornoy, I Dynnikov, D Rolfsen, B Wiest, Ordering braids, Math. Surveys and Monogr. 148, Amer. Math. Soc. (2008) MR2463428
11	A Fathi, F Laudenbach, V Poenaru, editors, Travaux de Thurston sur les surfaces, Astérisque 66–67, Soc. Math. France (1979) 284 MR568308
12	R Fenn, M T Greene, D Rolfsen, C Rourke, B Wiest, Ordering the braid groups, Pacific J. Math. 191 (1999) 49 MR1725462
13	J Fromentin, Every braid admits a short sigma-definite representative, to appear in J. Eur. Math. Soc. arXiv:0811.3902
14	T Ito, Braid ordering and knot genus, to appear in J. Knot Theory Ramifications arXiv:0805.2042
15	T Ito, Finite Thurston type orderings on dual braid monoids, to appear in J. Knot Theory Ramifications arXiv:0902.0833
16	J E Los, Knots, braid index and dynamical type, Topology 33 (1994) 257 MR1273785
17	A V Malyutin, Twist number of (closed) braids, St.Peterburg Math. J. 16 (2005) 791 MR2106667
18	A V Malyutin, N Y Netsvetaev, Dehornoy order in the braid group and transformations of closed braids, Algebra i Analiz 15 (2003) 170 MR2052167
19	W W Menasco, An addendum to iterated torus knots arXiv:math.GT/0610566
20	W W Menasco, On iterated torus knots and transversal knots, Geom. Topol. 5 (2001) 651 MR1857523
21	H Short, B Wiest, Orderings of mapping class groups after Thurston, Enseign. Math. $(2)$ 46 (2000) 279 MR1805402