On boundary slopes of immersed incompressible surfaces
نویسندگان
چکیده
منابع مشابه
Incompressible Maps of Surfaces: Boundary Slopes and Dehn Filling
The best understood 3-manifolds are Haken 3-manifolds; these are manifolds that are irreducible and contain incompressible surfaces. One approach to 3-manifolds is to try to generalize the notion of an incompressible surface. Essential laminations and mapped-in π1-injective surfaces have both been used with some success as substitutes for incompressible surfaces, yielding theorems which apply t...
متن کاملImmersed , Virtually - Embedded , Boundary Slopes
For the figure eight knot, we show that slopes with even numerator are slopes of immersed surfaces covered by incompressible, boundary-incompressible embeddings in some finite cover. 2000 Elsevier Science B.V. All rights reserved.
متن کاملOn Finiteness of the Number of Boundary Slopes of Immersed Surfaces in 3-manifolds
For any hyperbolic 3-manifold M with totally geodesic boundary, there are finitely many boundary slopes for essential immersed surfaces of a given genus. There is a uniform bound for the number of such boundary slopes if the genus of ∂M or the volume of M is bounded above. When the volume is bounded above, then area of ∂M is bounded above and the length of closed geodesic on ∂M is bounded below...
متن کاملT ] 1 0 N ov 1 99 9 Boundary slopes of immersed surfaces in 3 - manifolds
This paper presents some finiteness results for the number of boundary slopes of immersed proper π1-injective surfaces of given genus g in a compact 3-manifold with torus boundary. In the case of hyperbolic 3manifolds we obtain uniform quadratic bounds in g, independent of the 3-manifold.
متن کاملBoundary Curves of Incompressible Surfaces
Let M be an compact orientable 3 manifold whose boundary ∂M consists of a single torus. If a meridian and longitude in this torus are chosen, then isotopy classes of smoothly embedded circles in ∂M that do not bound disks correspond bijectively with elements of QP = Q ∪ {1/0} , regarded as slopes of these curves. We show in this paper that the set of slopes coming from boundary curves of incomp...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 1996
ISSN: 0373-0956
DOI: 10.5802/aif.1555