Mathematics Colloquia and Seminars

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Every 3-manifold has a co-dimension one foliation. A foliation is called taut if there exists a simple closed curve in the manifold that intersects each leaf of the foliation transversally. A surface bundle over a circle is the simplest example of a 3-manifold with a taut foliation. Every 3-manifold can be obtained from a surface bundle by Dehn filling the boundary components (with solid tori). We have proved that the fiber structure of a surface bundle can be perturbed to taut foliations realizing all rational boundary slopes in a neighbourhood of the the boundary slopes the fiber. This allowed us to prove that 3-manifolds obtained by Dehn-filling a surface-bundle along slopes sufficiently close to the slopes of the fiber produce closed 3-manifolds that contain taut foliations. This is a generalization of a result of Rachel Roberts to compact manifolds with disconnected boundary, and is also joint work with her.