Volume 9, issue 1 (2009)

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Circular thin position for knots in $S^3$

Fabiola Manjarrez-Gutiérrez

Algebraic & Geometric Topology 9 (2009) 429–454
Bibliography
1 G Burde, H Zieschang, Neuwirthsche Knoten und Flächenabbildungen, Abh. Math. Sem. Univ. Hamburg 31 (1967) 239 MR0229229
2 A J Casson, C M Gordon, Reducing Heegaard splittings, Topology Appl. 27 (1987) 275 MR918537
3 D Gabai, The Murasugi sum is a natural geometric operation, from: "Low-dimensional topology (San Francisco, Calif., 1981)" (editor S J Lomonaco Jr), Contemp. Math. 20, Amer. Math. Soc. (1983) 131 MR718138
4 D Gabai, Foliations and the topology of $3$–manifolds. III, J. Differential Geom. 26 (1987) 479 MR910018
5 H Goda, On handle number of Seifert surfaces in $S^3$, Osaka J. Math. 30 (1993) 63 MR1200821
6 H Goda, Circle valued Morse theory for knots and links, from: "Floer homology, gauge theory, and low-dimensional topology" (editors D A Ellwood, P S Ozsváth, A I Stipsicz, Z Szabó), Clay Math. Proc. 5, Amer. Math. Soc. (2006) 71 MR2249249
7 J Johnson, A Thompson, On tunnel number one knots that are not $(1,n)$ arXiv:math/0606226v3
8 Y Matsumoto, An introduction to Morse theory, Transl. of Math. Monogr. 208, Amer. Math. Soc. (2002) MR1873233
9 J Milnor, Morse theory, Annals of Math. Studies 51, Princeton Univ. Press (1963) MR0163331
10 S P Novikov, Multivalued functions and functionals. An analogue of the Morse theory, Dokl. Akad. Nauk SSSR 260 (1981) 31 MR630459
11 A V Pajitnov, Circle-valued Morse theory, de Gruyter Studies in Math. 32, de Gruyter (2006) MR2319639
12 A Ranicki, Circle valued Morse theory and Novikov homology, from: "Topology of high-dimensional manifolds, No. 1, 2 (Trieste, 2001)" (editors T F Farrell, L Göttsche, W Lück), ICTP Lect. Notes 9, Abdus Salam Int. Cent. Theoret. Phys. (2002) 539 MR1937024
13 D Rolfsen, Knots and links, Math. Lecture Ser. 7, Publish or Perish (1976) MR0515288
14 M Scharlemann, J Schultens, Annuli in generalized Heegaard splittings and degeneration of tunnel number, Math. Ann. 317 (2000) 783 MR1777119
15 M Scharlemann, A Thompson, Thin position for $3$–manifolds, from: "Geometric topology (Haifa, 1992)" (editors C Gordon, Y Moriah, B Wajnryb), Contemp. Math. 164, Amer. Math. Soc. (1994) 231 MR1282766
16 K Veber, A Pazhitnov, L Rudolf, The Morse–Novikov number for knots and links, Algebra i Analiz 13 (2001) 105 MR1850189
17 F Waldhausen, On irreducible $3$–manifolds which are sufficiently large, Ann. of Math. $(2)$ 87 (1968) 56 MR0224099
18 W Whitten, Isotopy types of knot spanning surfaces, Topology 12 (1973) 373 MR0372842