Sums of incompressible surfaces

Oertel, Ulrich

doi:10.1090/S0002-9939-1988-0929008-9

Sums of incompressible surfaces
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Proc. Amer. Math. Soc. 102 (1988), 711-719 Request permission

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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