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On surfaces and Heegaard surfaces
Author:
Klaus Johannson
Journal:
Trans. Amer. Math. Soc. 325 (1991), 573-591
MSC:
Primary 57N10; Secondary 57N05
MathSciNet review:
1064268
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Abstract: This paper is concerned with the intersection of surfaces and Heegaard surfaces in closed orientable  -manifolds  . Given a Heegaard decomposition  it will be shown that any surface (orientable or not) in  is equivalent to a surface which intersects  in discs whose total number is limited from above by some function in the genus of  alone. The equivalence relation in question is generated by disc- and annulus-compressions.
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Haken, Theorie der Normalflächen, Acta Math.
105 (1961), 245–375 (German). MR 0141106
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-, Some results on surfaces in
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551744 (82c:57005)
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- [Ha 1]
- W. Haken, Theorie der Normalflächen, Acta Math. 105 (1961), 245-375. MR 0141106 (25:4519a)
- [Ha 2]
- -, Some results on surfaces in -manifolds, Studies in Modern Topology, Math. Assoc. Amer. (distributed by Prentice-Hall), 1968.
- [He]
- J. Hempel,
 -manifolds, Ann. of Math. Studies, no. 86, Princeton Univ. Press, 1976. MR 0415619 (54:3702)
- [Joh 1]
- K. Johannson, Homotopy equivalences of
 -manifolds with boundaries, Lecture Notes in Math., vol. 761, Springer, 1979. MR 551744 (82c:57005)
- [Joh 2]
- -, On surfaces in one-relator -manifolds, London Math. Soc. Lecture Note Ser. 112, LMS, 1986, pp. 157-192.
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- -, Computations in -manifolds, preprint 1991.
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- T. Kobayashi, Non-separating incompressible tori in
 -manifolds, J. Math. Soc. Japan 36 (1984), 11-22. MR 723589 (85a:57008)
- [Ko 2]
- -, Heegaard genera and torus decomposition of Haken -manifolds, MSRI Berkeley preprint series, 1985.
- [Och]
- M. Ochiai, On Haken's theorem and its extension, Osaka J. Math. 20 (1983), 461-468. MR 706246 (85c:57014)
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- F. Waldhausen, Eine Klasse von dreidimensionalen Mannigfaltigkeiten I, Invent. Math. 3 (1967), 308-333; II, ibid. 4 (1967), 87-117. MR 0235576 (38:3880)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1991-1064268-2
PII:
S 0002-9947(1991)1064268-2
Article copyright:
© Copyright 1991 American Mathematical Society
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