Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Sums of incompressible surfaces

Author: Ulrich Oertel
Journal: Proc. Amer. Math. Soc. 102 (1988), 711-719
MSC: Primary 57N10
MathSciNet review: 929008
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In an orientable Haken $ 3$-manifold, given two orientable incompressible surfaces $ F$ and $ S$ transverse to each other with intersections suitably simplified, certain cut-and-paste operations along curves of intersection yield embedded incompressible surfaces. We show in this paper that, no matter how $ F$ and $ S$ are isotoped, as long as intersections are suitably simplified, exactly the same finite (possibly empty) set of isotopy classes of incompressible surfaces result from cut-and-paste operations.

References [Enhancements On Off] (What's this?)

  • [FH] W. Floyd and A. Hatcher, The space of incompressible surfaces in a $ 2$-bridge link complement, Trans. Amer. Math. Soc. 305 (1988), 575-599. MR 924770 (89c:57004)
  • [FO] W. Floyd and U. Oertel, Incompressible branched surfaces via branched surfaces, Topology 23 (1984), 117-125. MR 721458 (85a:57007)
  • [H] W. Haken, Theorie der Normalflaechen, Acta Math. 105 (1961), 245-375. MR 0141106 (25:4519a)
  • [H1] A. Hatcher, Homeomorphisms of sufficiently large $ {P^2}$-irreducible $ 3$-manifolds, Topology 15 (1976), 343-347. MR 0420620 (54:8633)
  • [H2] -, On the diffeomorphism group of $ {S^1} \times {S^2}$, Proc. Amer. Math. Soc. 83 (1981), 427-430. MR 624946 (83i:57022)
  • [JO] W. Jaco and U. Oertel, An algorithm to determine if a $ 3$-manifold is a Haken manifold, Topology 23 (1984), 195-209. MR 744850 (85j:57014)
  • [O1] U. Oertel, Incompressible branched surfaces, Invent. Math. 76 (1984), 385-410. MR 746535 (86a:57007)
  • [O2] -, Measured laminations in $ 3$-manifolds, Trans. Amer. Math. Soc. 305 (1988), 531-575. MR 924769 (89d:57011)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57N10

Retrieve articles in all journals with MSC: 57N10

Additional Information

Keywords: Incompressible surface, incompressible branched surface, Haken manifold, projective lamination space
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society