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The algebraic crossing number and the braid index of knots and links

Keiko Kawamuro

Algebraic & Geometric Topology 6 (2006) 2313–2350
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 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, W W Menasco, Studying links via closed braids. IV. Composite links and split links, Invent. Math. 102 (1990) 115 MR1069243
4 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
5 J S Birman, W W Menasco, Stabilization in the braid groups. I. MTWS, Geom. Topol. 10 (2006) 413 MR2224463
6 J Franks, R F Williams, Braids and the Jones polynomial, Trans. Amer. Math. Soc. 303 (1987) 97 MR896009
7 E Giroux, Géométrie de contact: de la dimension trois vers les dimensions supérieures, from: "Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002)", Higher Ed. Press (2002) 405 MR1957051
8 V F R Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. $(2)$ 126 (1987) 335 MR908150
9 K Kawamuro, Conjectures on the braid index and the algebraic crossing number
10 W B R Lickorish, An introduction to knot theory, Graduate Texts in Mathematics 175, Springer (1997) MR1472978
11 P M Melvin, H R Morton, Fibred knots of genus $2$ formed by plumbing Hopf bands, J. London Math. Soc. $(2)$ 34 (1986) 159 MR859157
12 H R Morton, Seifert circles and knot polynomials, Math. Proc. Cambridge Philos. Soc. 99 (1986) 107 MR809504
13 H R Morton, H B Short, The $2$-variable polynomial of cable knots, Math. Proc. Cambridge Philos. Soc. 101 (1987) 267 MR870598
14 K Murasugi, On the braid index of alternating links, Trans. Amer. Math. Soc. 326 (1991) 237 MR1000333
15 W D Neumann, Private communication
16 W D Neumann, L Rudolph, Difference index of vectorfields and the enhanced Milnor number, Topology 29 (1990) 83 MR1046626
17 W D Neumann, D Zagier, Volumes of hyperbolic three-manifolds, Topology 24 (1985) 307 MR815482
18 A Stoimenow, Properties of closed $3$-braids arXiv:math.GT/0606435
19 A Stoimenow, On the crossing number of positive knots and braids and braid index criteria of Jones and Morton-Williams-Franks, Trans. Amer. Math. Soc. 354 (2002) 3927 MR1926860
20 R F Williams, The braid index of generalized cables, Pacific J. Math. 155 (1992) 369 MR1178031
21 P Xu, The genus of closed $3$-braids, J. Knot Theory Ramifications 1 (1992) 303 MR1180404