Heegaard surfaces in Haken 3-manifolds
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- by Klaus Johannson PDF
- Bull. Amer. Math. Soc. 23 (1990), 91-98
References
- Joan S. Birman, F. González-Acuña, and José M. Montesinos, Heegaard splittings of prime $3$-manifolds are not unique, Michigan Math. J. 23 (1976), no. 2, 97–103. MR 431175
- Michel Boileau, Markus Rost, and Heiner Zieschang, Décompositions de Heegaard des extérieurs des nœuds toriques et des variétés de Seifert associées, C. R. Acad. Sci. Paris Sér. I Math. 302 (1986), no. 18, 661–664 (French, with English summary). MR 847514
- Francis Bonahon, Difféotopies des espaces lenticulaires, Topology 22 (1983), no. 3, 305–314 (French). MR 710104, DOI 10.1016/0040-9383(83)90016-2
- Francis Bonahon and Jean-Pierre Otal, Scindements de Heegaard des espaces lenticulaires, C. R. Acad. Sci. Paris Sér. I Math. 294 (1982), no. 17, 585–587 (French, with English summary). MR 663085
- Iván Cardona and Wolfgang Heil, Essential tori and Klein bottles in nonorientable 3-manifolds of genus two, Geometry and topology, World Sci. Publishing, Singapore, 1989, pp. 31–57. MR 1001587
- Charles Frohman and Joel Hass, Unstable minimal surfaces and Heegaard splittings, Invent. Math. 95 (1989), no. 3, 529–540. MR 979363, DOI 10.1007/BF01393888
- Wolfgang Haken, Theorie der Normalflächen, Acta Math. 105 (1961), 245–375 (German). MR 141106, DOI 10.1007/BF02559591
- Wolfgang Haken, Über das Homöomorphieproblem der 3-Mannigfaltigkeiten. I, Math. Z. 80 (1962), 89–120 (German). MR 160196, DOI 10.1007/BF01162369
- Wolfgang Haken, Some results on surfaces in $3$-manifolds, Studies in Modern Topology, Math. Assoc. America, Buffalo, N.Y.; distributed by Prentice-Hall, Englewood Cliffs, N.J., 1968, pp. 39–98. MR 0224071
- Geoffrey Hemion, On the classification of homeomorphisms of $2$-manifolds and the classification of $3$-manifolds, Acta Math. 142 (1979), no. 1-2, 123–155. MR 512214, DOI 10.1007/BF02395059
- William Jaco, Adding a $2$-handle to a $3$-manifold: an application to property $R$, Proc. Amer. Math. Soc. 92 (1984), no. 2, 288–292. MR 754723, DOI 10.1090/S0002-9939-1984-0754723-6
- William H. Jaco and Peter B. Shalen, Seifert fibered spaces in $3$-manifolds, Mem. Amer. Math. Soc. 21 (1979), no. 220, viii+192. MR 539411, DOI 10.1090/memo/0220
- Klaus Johannson, Homotopy equivalences of $3$-manifolds with boundaries, Lecture Notes in Mathematics, vol. 761, Springer, Berlin, 1979. MR 551744, DOI 10.1007/BFb0085406
- Klaus Johannson, On surfaces in one-relator $3$-manifolds, Low-dimensional topology and Kleinian groups (Coventry/Durham, 1984) London Math. Soc. Lecture Note Ser., vol. 112, Cambridge Univ. Press, Cambridge, 1986, pp. 157–192. MR 903864 [Joh3] K. Johannson, Computations in 3-manifolds, preprint. [Joh4] K. Johannson, On the Reidemeister-Singer theorem, preprint.
- Tsuyoshi Kobayashi, Nonseparating incompressible tori in $3$-manifolds, J. Math. Soc. Japan 36 (1984), no. 1, 11–22. MR 723589, DOI 10.2969/jmsj/03610011
- Edwin E. Moise, Affine structures in $3$-manifolds. V. The triangulation theorem and Hauptvermutung, Ann. of Math. (2) 56 (1952), 96–114. MR 48805, DOI 10.2307/1969769
- Mitsuyuki Ochiai, On Haken’s theorem and its extension, Osaka J. Math. 20 (1983), no. 2, 461–468. MR 706246
- Józef H. Przytycki, Incompressibility of surfaces after Dehn surgery, Michigan Math. J. 30 (1983), no. 3, 289–308. MR 725782, DOI 10.1307/mmj/1029002906 [Re] K. Reidemeister, Zur dreidimensionalen Topologie, Abh. Math. Sem. Univ. Hamburg 9 (1936), 189-194.
- James Singer, Three-dimensional manifolds and their Heegaard diagrams, Trans. Amer. Math. Soc. 35 (1933), no. 1, 88–111. MR 1501673, DOI 10.1090/S0002-9947-1933-1501673-5
- Martin Scharlemann, The Thurston norm and $2$-handle addition, Proc. Amer. Math. Soc. 100 (1987), no. 2, 362–366. MR 884480, DOI 10.1090/S0002-9939-1987-0884480-7
- Friedhelm Waldhausen, Heegaard-Zerlegungen der $3$-Sphäre, Topology 7 (1968), 195–203 (German). MR 227992, DOI 10.1016/0040-9383(68)90027-X
- Friedhelm Waldhausen, Some problems on $3$-manifolds, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 313–322. MR 520549
- H. Cišang, On the classification of simple systems of paths on a surface of genus $2$, Dokl. Akad. Nauk SSSR 152 (1963), 841–844 (Russian). MR 0179782
Additional Information
- Journal: Bull. Amer. Math. Soc. 23 (1990), 91-98
- MSC (1985): Primary 57M99
- DOI: https://doi.org/10.1090/S0273-0979-1990-15910-5
- MathSciNet review: 1027902