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A new algorithm for recognizing the unknot

Joan S Birman and Michael D Hirsch

Geometry & Topology 2 (1998) 175–220

DOI: 10.2140/gt.1998.2.175

Bibliography
1 D Bennequin, Entrelacements et équations de Pfaff, from: "Third Schnepfenried geometry conference, Vol. 1 (Schnepfenried, 1982)", Astérisque 107, Soc. Math. France (1983) 87–161 MR753131
2 J S Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies 82, Princeton University Press (1974) MR0375281
3 J S Birman, E Finkelstein, Studying surfaces via closed braids, J. Knot Theory Ramifications 7 (1998) 267–334 MR1625362
4 J Birman, K H Ko, S J Lee, A new approach to the word and conjugacy problems in the braid groups, Adv. Math. 139 (1998) 322–353 MR1654165
5 J S Birman, W W Menasco, Studying links via closed braids V: The unlink, Trans. Amer. Math. Soc. 329 (1992) 585–606 MR1030509
6 E A El-Rifai, H R Morton, Algorithms for positive braids, Quart. J. Math. Oxford Ser. (2) 45 (1994) 479–497 MR1315459
7 F A Garside, The braid group and other groups, Quart. J. Math. Oxford Ser. (2) 20 (1969) 235–254 MR0248801
8 W Haken, Theorie der Normalflächen, Acta Math. 105 (1961) 245–375 MR0141106
9 J Hass, Algorithms for recognizing knots and 3–manifolds, Chaos Solitons Fractals 9 (1998) 569–581 MR1628743 Knot theory and its applications
10 J Hass, J C Lagarias, N Pippenger, The computational complexity of knot and link problems, J. ACM 46 (1999) 185–211 MR1693203
11 F Jaeger, D L Vertigan, D J A Welsh, On the computational complexity of the Jones and Tutte polynomials, Math. Proc. Cambridge Philos. Soc. 108 (1990) 35–53 MR1049758
12 E S Kang, K H Ko, S J Lee, Band-generator presentation for the 4–braid group, Topology Appl. 78 (1997) 39–60 MR1465024 Special issue on braid groups and related topics (Jerusalem, 1995)
13 P Vogel, Representation of links by braids: a new algorithm, Comment. Math. Helv. 65 (1990) 104–113 MR1036132
14 P Xu, The genus of closed 3–braids, J. Knot Theory Ramifications 1 (1992) 303–326 MR1180404
15 S Yamada, The minimal number of Seifert circles equals the braid index of a link, Invent. Math. 89 (1987) 347–356 MR894383