Volume 10, issue 1 (2006)

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

Volume 23
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
Stabilization in the braid groups I: MTWS

Joan S Birman and William W Menasco

Geometry & Topology 10 (2006) 413–540
Bibliography
1 J W Alexander, A lemma on systems of knotted curves, Proc. Nat. Acad. Sci. USA 9 (1923) 93
2 D Bennequin, Entrelacements et équations de Pfaff, from: "Third Schnepfenried geometry conference, Vol. 1 (Schnepfenried, 1982)", Astérisque 107, Soc. Math. France (1983) 87 MR753131
3 J S Birman, Braids, links, and mapping class groups, Princeton University Press (1974) MR0375281
4 J S Birman, E Finkelstein, Studying surfaces via closed braids, J. Knot Theory Ramifications 7 (1998) 267 MR1625362
5 J S Birman, M D Hirsch, A new algorithm for recognizing the unknot, Geom. Topol. 2 (1998) 175 MR1658024
6 J S Birman, W W Menasco, Stabilization in the braid groups II: Applications to transverse knots, arXiv:math.GT/0310280
7 J S Birman, W W Menasco, Studying links via closed braids IV : Composite links and split links, Invent. Math. 102 (1990) 115 MR1069243
8 J S Birman, W W Menasco, Studying links via closed braids I : A finiteness theorem, Pacific J. Math. 154 (1992) 17 MR1154731
9 J S Birman, W W Menasco, Studying links via closed braids V : The unlink, Trans. Amer. Math. Soc. 329 (1992) 585 MR1030509
10 J S Birman, W W Menasco, Studying links via closed braids VI : A nonfiniteness theorem, Pacific J. Math. 156 (1992) 265 MR1186805
11 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
12 J S Birman, W W Menasco, On Markov’s theorem, J. Knot Theory Ramifications 11 (2002) 295 MR1905686
13 J S Birman, M Rampichini, P Boldi, S Vigna, Towards an implementation of the B–H algorithm for recognizing the unknot, J. Knot Theory Ramifications 11 (2002) 601 MR1915499
14 J S Birman, N C Wrinkle, On transversally simple knots, J. Differential Geom. 55 (2000) 325 MR1847313
15 G Burde, H Zieschang, Knots, 5, Walter de Gruyter & Co. (1985) MR808776
16 P R Cromwell, Embedding knots and links in an open book I : Basic properties, Topology Appl. 64 (1995) 37 MR1339757
17 I Dynnikov, Arc presentations of links: monotonic simplification, arXiv:math.GT/0208153
18 T Fiedler, A small state sum for knots, Topology 32 (1993) 281 MR1217069
19 J Hempel, 3–Manifolds, Princeton University Press (1976) MR0415619
20 K Kawamuro, Failure of the Morton–Franks–Williams inequality, arXiv:math.GT/0509169
21 R Kirby, A calculus for framed links in S3, Invent. Math. 45 (1978) 35 MR0467753
22 S Lambropoulou, C P Rourke, Markov’s theorem in 3–manifolds, Topology Appl. 78 (1997) 95 MR1465027
23 A A Markov, Uber die freie Aquivalenz geschlossener Zopfe, Recueil Mathematique Moscou 1 (1935) 73
24 W W Menasco, Closed braids and Heegaard splittings, from: "Knots, braids, and mapping class groups—papers dedicated to Joan S. Birman (New York, 1998)", AMS/IP Stud. Adv. Math. 24, Amer. Math. Soc. (2001) 131 MR1873114
25 W W Menasco, On iterated torus knots and transversal knots, Geom. Topol. 5 (2001) 651 MR1857523
26 H R Morton, Infinitely many fibred knots having the same Alexander polynomial, Topology 17 (1978) 101 MR486796
27 H R Morton, An irreducible 4–string braid with unknotted closure, Math. Proc. Cambridge Philos. Soc. 93 (1983) 259 MR691995
28 H R Morton, Threading knot diagrams, Math. Proc. Cambridge Philos. Soc. 99 (1986) 247 MR817666
29 M Scharlemann, A Thompson, Thin position and Heegaard splittings of the 3–sphere, J. Differential Geom. 39 (1994) 343 MR1267894
30 J Singer, Three-dimensional manifolds and their Heegaard diagrams, Trans. Amer. Math. Soc. 35 (1933) 88 MR1501673
31 P Traczyk, A new proof of Markov’s braid theorem, from: "Knot theory (Warsaw, 1995)", Banach Center Publ. 42, Polish Acad. Sci. (1998) 409 MR1634469
32 F Waldhausen, Heegaard–Zerlegungen der 3–Sphäre, Topology 7 (1968) 195 MR0227992
33 J Zablow, Loops, waves and an algebra for Heegaard splittings, PhD thesis, City University of New York (1999)