Intersection of surfaces in 3-manifolds

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Given a pair of incompressible surfaces F and S in an irreducible 3-manifold M, we define a directed graph T which expresses the way F may be isotoped with respect to S. We study the properties of T. We use our results about T to study properties of the intersection between F and S.

Original languageEnglish
Pages (from-to)15-61
Number of pages47
JournalTopology and its Applications
Issue number1
StatePublished - 1999
Externally publishedYes


  • 3-manifolds
  • Incompressible surfaces
  • Isotopy


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