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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
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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.

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

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