Algebraic & Geometric Topology Volume 6, issue 5 (2006)

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Genus generators and the positivity of the signature

Alexander Stoimenow

Algebraic & Geometric Topology 6 (2006) 2351–2393

DOI: 10.2140/agt.2006.6.2351

Bibliography

1	N A’Campo, Generic immersions of curves, knots, monodromy and Gordian number, Inst. Hautes Études Sci. Publ. Math. (1998) MR1733329
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	M Boileau, C Weber, Le problème de J. Milnor sur le nombre gordien des n\oe uds algébriques, Enseign. Math. $(2)$ 30 (1984) 173 MR767901
4	M Brittenham, Bounding canonical genus bounds volume
5	J M van Buskirk, Positive knots have positive Conway polynomials, from: "Knot theory and manifolds (Vancouver, 1983)", Lecture Notes in Math. 1144, Springer (1985) 146 MR823288
6	T D Cochran, Noncommutative knot theory, Algebr. Geom. Topol. 4 (2004) 347 MR2077670
7	T D Cochran, R E Gompf, Applications of Donaldson's theorems to classical knot concordance, homology $3$-spheres and property $P$, Topology 27 (1988) 495 MR976591
8	J H Conway, An enumeration of knots and links, and some of their algebraic properties, from: "Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967)", Pergamon (1970) 329 MR0258014
9	P R Cromwell, Homogeneous links, J. London Math. Soc. $(2)$ 39 (1989) 535 MR1002465
10	P R Cromwell, Positive braids are visually prime, Proc. London Math. Soc. $(3)$ 67 (1993) 384 MR1226607
11	R Crowell, Genus of alternating link types, Ann. of Math. $(2)$ 69 (1959) 258 MR0099665
12	R Fintushel, R J Stern, Pseudofree orbifolds, Ann. of Math. $(2)$ 122 (1985) 335 MR808222
13	J Franks, R F Williams, Braids and the Jones polynomial, Trans. Amer. Math. Soc. 303 (1987) 97 MR896009
14	D Gabai, Foliations and genera of links, Topology 23 (1984) 381 MR780731
15	C M Gordon, R A Litherland, K Murasugi, Signatures of covering links, Canad. J. Math. 33 (1981) 381 MR617628
16	M Hirasawa, The flat genus of links, Kobe J. Math. 12 (1995) 155 MR1391192
17	F Hirzebruch, Singularities and exotic spheres, from: "Séminaire Bourbaki, Vol. 10", Soc. Math. France (1995) 13 MR1610436
18	T Kawamura, Relations among the lowest degree of the Jones polynomial and geometric invariants for a closed positive braid, Comment. Math. Helv. 77 (2002) 125 MR1898395
19	D Kreimer, Knots and Feynman diagrams, Cambridge Lecture Notes in Physics 13, Cambridge University Press (2000) MR1778151
20	P B Kronheimer, T S Mrowka, The genus of embedded surfaces in the projective plane, Math. Res. Lett. 1 (1994) 797 MR1306022
21	J Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969) 229 MR0246314
22	W W Menasco, M B Thistlethwaite, The Tait flyping conjecture, Bull. Amer. Math. Soc. $($N.S.$)$ 25 (1991) 403 MR1098346
23	K Murasugi, On the genus of the alternating knot. I, II, J. Math. Soc. Japan 10 (1958) 94, 235 MR0099664
24	K Murasugi, On a certain subgroup of the group of an alternating link, Amer. J. Math. 85 (1963) 544 MR0157375
25	K Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc. 117 (1965) 387 MR0171275
26	T Nakamura, Positive alternating links are positively alternating, J. Knot Theory Ramifications 9 (2000) 107 MR1749503
27	M Ozawa, Closed incompressible surfaces in the complements of positive knots, Comment. Math. Helv. 77 (2002) 235 MR1915040
28	P Ozsváth, Z Szabó, Knot Floer homology and the four-ball genus, Geom. Topol. 7 (2003) 615 MR2026543
29	J Rasmussen, Khovanov homology and the slice genus arXiv:math.GT/0402131
30	D Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish (1976) MR0515288
31	L Rudolph, Nontrivial positive braids have positive signature, Topology 21 (1982) 325 MR649763
32	L Rudolph, Quasipositivity as an obstruction to sliceness, Bull. Amer. Math. Soc. $($N.S.$)$ 29 (1993) 51 MR1193540
33	L Rudolph, Positive links are strongly quasipositive, from: "Proceedings of the Kirbyfest (Berkeley, CA, 1998)" (editors J Hass, M Scharlemann), Geom. Topol. Monogr. 2 (1999) 555 MR1734423
34	A Stoimenow, Bennequin's inequality and the positivity of the signature
35	A Stoimenow, Diagram genus, generators and applications
36	A Stoimenow, Knots of genus two arXiv:math.GT/0303012
37	A Stoimenow, On the crossing number of semiadequate links
38	A Stoimenow, The signature of 2-almost positive knots, J. Knot Theory Ramifications 9 (2000) 813 MR1775388
39	A Stoimenow, Knots of genus one or on the number of alternating knots of given genus, Proc. Amer. Math. Soc. 129 (2001) 2141 MR1825928
40	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
41	A Stoimenow, The crossing number and maximal bridge length of a knot diagram, Pacific J. Math. 210 (2003) 189 MR1989075
42	A Stoimenow, Positive knots, closed braids and the Jones polynomial, Ann. Sc. Norm. Super. Pisa Cl. Sci. $(5)$ 2 (2003) 237 MR2004964
43	A Stoimenow, Gau\ss diagram sums on almost positive knots, Compos. Math. 140 (2004) 228 MR2004131
44	A Stoimenow, V Tchernov, A Vdovina, The canonical genus of a classical and virtual knot, Geom. Dedicata 95 (2002) 215 MR1950891
45	A Stoimenow, A Vdovina, Counting alternating knots by genus, Math. Ann. 333 (2005) 1 MR2169826
46	K Taniyama, A partial order of knots, Tokyo J. Math. 12 (1989) 205 MR1001742
47	P Traczyk, Nontrivial negative links have positive signature, Manuscripta Math. 61 (1988) 279 MR949818
48	P Vogel, Representation of links by braids: a new algorithm, Comment. Math. Helv. 65 (1990) 104 MR1036132
49	R F Williams, Lorenz knots are prime, Ergodic Theory Dynam. Systems 4 (1984) 147 MR758900
50	S Yamada, The minimal number of Seifert circles equals the braid index of a link, Invent. Math. 89 (1987) 347 MR894383
51	Y Yokota, Polynomial invariants of positive links, Topology 31 (1992) 805 MR1191382