Algebraic & Geometric Topology Volume 9, issue 1 (2009)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Interests

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author Index

To Appear

Other MSP Journals

Lens space surgeries as A'Campo's divide knots

Yuichi Yamada

Algebraic & Geometric Topology 9 (2009) 397–428

DOI: 10.2140/agt.2009.9.397

Bibliography

1	N A’Campo, Le groupe de monodromie du déploiement des singularités isolées de courbes planes. I, Math. Ann. 213 (1975) 1 MR0377108
2	N A’Campo, Generic immersions of curves, knots, monodromy and Gordian number, Inst. Hautes Études Sci. Publ. Math. (1998) MR1733329
3	N A’Campo, Planar trees, slalom curves and hyperbolic knots, Inst. Hautes Études Sci. Publ. Math. (1998) MR1733330
4	N A’Campo, Real deformations and complex topology of plane curve singularities, Ann. Fac. Sci. Toulouse Math. $(6)$ 8 (1999) 5 MR1721511
5	V I Arnol′d, S M Guseĭn-Zade, A N Varchenko, Singularities of differentiable maps. Vol. II. Monodromy and asymptotics of integrals, Monogr. in Math. 83, Birkhäuser (1988) MR966191
6	J Bailey, D Rolfsen, An unexpected surgery construction of a lens space, Pacific J. Math. 71 (1977) 295 MR0488061
7	K L Baker, Knots on once-punctured torus fibers, PhD thesis, University of Texas at Austin (2004)
8	K L Baker, Surgery descriptions and volumes of Berge knots. I. Large volume Berge knots, J. Knot Theory Ramifications 17 (2008) 1077 MR2457837
9	K L Baker, Surgery descriptions and volumes of Berge knots. II. Descriptions on the minimally twisted five chain link, J. Knot Theory Ramifications 17 (2008) 1099 MR2457838
10	J Berge, Some knots with surgeries yielding lens spaces, Unpublished manuscript (1990)
11	J Berge, The knots in $D^2\times S^1$ which have nontrivial Dehn surgeries that yield $D^2\times S^1$, Topology Appl. 38 (1991) 1 MR1093862
12	S Chmutov, Diagrams of divide links, Proc. Amer. Math. Soc. 131 (2003) 1623 MR1950295
13	O Couture, B Perron, Representative braids for links associated to plane immersed curves, J. Knot Theory Ramifications 9 (2000) 1 MR1749500
14	M Culler, C M Gordon, J Luecke, P B Shalen, Dehn surgery on knots, Ann. of Math. $(2)$ 125 (1987) 237 MR881270
15	J Dean, Hyperbolic knots with small Seifert-fibered Dehn surgeries, PhD thesis, University of Texas at Austin (1996)
16	A Deruelle, K Miyazaki, K Motegi, Networking Seifert fibered surgeries on knots, Preprint
17	R Fintushel, R J Stern, Constructing lens spaces by surgery on knots, Math. Z. 175 (1980) 33 MR595630
18	H Goda, M Hirasawa, Y Yamada, Lissajous curves as A'Campo divides, torus knots and their fiber surfaces, Tokyo J. Math. 25 (2002) 485 MR1948678
19	H Goda, M Teragaito, Dehn surgeries on knots which yield lens spaces and genera of knots, Math. Proc. Cambridge Philos. Soc. 129 (2000) 501 MR1780501
20	R E Gompf, A I Stipsicz, $4$–manifolds and Kirby calculus, Graduate Studies in Math. 20, Amer. Math. Soc. (1999) MR1707327
21	C M Gordon, Dehn surgery on knots, from: "Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990)", Math. Soc. Japan (1991) 631 MR1159250
22	C M Gordon, Dehn filling: a survey, from: "Knot theory (Warsaw, 1995)" (editors V F R Jones, J Kania-Bartoszyn’ska, J H Przytycki, P Traczyk, V G Turaev), Banach Center Publ. 42, Polish Acad. Sci. (1998) 129 MR1634453
23	S M Guseĭn-Zade, Intersection matrices for certain singularities of functions of two variables, Funkcional. Anal. i Priložen. 8 (1974) 11 MR0338437
24	J Harer, A Kas, R Kirby, Handlebody decompositions of complex surfaces, Mem. Amer. Math. Soc. 62 (1986) MR849942
25	M Hedden, Notions of positivity and the Ozváth–Szabó concordance invariant arXiv:math.GT/0509.499
26	M Hedden, On Floer homology and the Berge conjecture on knots admitting lens space surgeries arXiv:math.GT/0710.0357
27	P Hill, K Murasugi, On double-torus knots. II, J. Knot Theory Ramifications 9 (2000) 617 MR1762760
28	M Hirasawa, Visualization of A'Campo's fibered links and unknotting operation, from: "Proceedings of the First Joint Japan–Mexico Meeting in Topology (Morelia, 1999)", Topology Appl. 121 (2002) 287 MR1903697
29	R Kirby, A calculus for framed links in $S^{3}$, Invent. Math. 45 (1978) 35 MR0467753
30	N Maruyama, On Dehn surgery along a certain family of knots, J. Tsuda College (1987) 261 MR892642
31	K Morimoto, Y Yamada, A note on essential tori in the exterior of torus knots with twists, to appear in Kobe J. Math.
32	L Moser, Elementary surgery along a torus knot, Pacific J. Math. 38 (1971) 737 MR0383406
33	Y Ni, Knot Floer homology detects fibred knots, Invent. Math. 170 (2007) 577 MR2357503
34	R P Osborne, R S Stevens, Group presentations corresponding to spines of $3$–manifolds. III, Trans. Amer. Math. Soc. 234 (1977) 245 MR0488063
35	P Ozsváth, Z Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005) 1281 MR2168576
36	C V Quach Hongler, C Weber, The link of an extrovert divide, Ann. Fac. Sci. Toulouse Math. $(6)$ 9 (2000) 133 MR1815944
37	L Rudolph, Knot theory of complex plane curves, from: "Handbook of knot theory" (editors W Menasco, M Morwen Thistlethwaite), Elsevier B. V. (2005) 349 MR2179266
38	J R Stallings, Constructions of fibred knots and links, from: "Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., 1976), Part 2" (editor R J Milgram), Proc. Sympos. Pure Math. XXXII, Amer. Math. Soc. (1978) 55 MR520522
39	M Tange, Lens spaces given from L-space homology $3$–spheres arXiv:math.GT/0709.0141
40	M Teragaito, Dehn surgery on knots yielding lens spaces, Lecture (1999)
41	Y Yamada, Plane slalom curves of a certain type, pretzel links and Kirby-Melvin's Grapes (in Japanese), Sūri-Kaiseki-Kenkyū-Sho Kō-Kyū-Roku
42	Y Yamada, Berge's knots in the fiber surfaces of genus one, lens space and framed links, J. Knot Theory Ramifications 14 (2005) 177 MR2128509
43	Y Yamada, A family of knots yielding graph manifolds by Dehn surgery, Michigan Math. J. 53 (2005) 683 MR2207215
44	Y Yamada, Finite Dehn surgery along A'Campo's divide knots, from: "Singularity theory and its applications" (editors S Izumiya, G Ishikawa, H Tokunaga, I Shimada, T Sano), Adv. Stud. Pure Math. 43, Math. Soc. Japan (2006) 573 MR2325154