Taut foliation
WebThe boundary torus is another leaf of the Reeb foliation. Definition: A foliation F of codimension one on a closed manifold is called taut if one can embed into it a transverse circle that intersects each leaf. Theorem (Goodman [GO]): A codimension one foliation F of a closed 3-manifold is taut if and only if it does not have a Reeb Component. WebThe induced foliation of is called the n-dimensional Reeb foliation. Its leaf space is not Hausdorff. 2.5 Taut foliations . A codimension one foliation of is taut if for every leaf of there is a circle transverse to which intersects . 3 References [Godbillon1991] C. Godbillon, Feuilletages, Birkhäuser Verlag, 1991.
Taut foliation
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WebThe foliation F is everywhere taut, or simply taut, if for every point p of M there is a simple closed transversal to F that contains p. In the absence of sufficient smoothness, these three notions of tautness differ, and they are frequently confused in the literature. WebMar 19, 2002 · If M is an atoroidal 3-manifold with a taut foliation, Thurston showed that pi_1(M) acts on a circle. Here, we show that some other classes of essential laminations also give rise to actions on circles. In particular, we show this for tight essential laminations with solid torus guts. We also show that pseudo-Anosov flows induce actions on circles. …
WebDec 8, 2024 · Let \(\mathscr {F}\) be a cooriented taut foliation in a closed 3-manifold M. Suppose that \(\mathscr {F}\) has a leaf homeomorphic to S 2. Then M is homeomorphic to S 2 × S 1 and \(\mathscr {F}\) is the product foliation by spheres. Sketch of the Proof. Since π 1 (S 2) is trivial, the holonomy along any path on the spherical leaf is trivial. WebFeb 1, 2024 · Let be a closed, orientable, and irreducible 3-manifold with Heegaard genus two. We prove that if the fundamental group of is left-orderable then admits a co …
WebMay 9, 2016 · De nition 2.7. A C1;0 foliation Fis smoothly taut if for every leaf Lof Fthere is a simple closed transversal to Fthat has nonempty intersection with L. De nition 2.8. Let Fbe … Weboriented foliation on M. See [Yaz20, Theorem 8.1] for this deduction, originally due to Wood. A transversely oriented foliation of a 3-manifold is taut if for every leaf L there is a circle cL intersecting L and transverse to the foliation. Manifolds that admit taut foliations have
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WebOct 1, 2015 · Then the foliation is non-taut if and only if there is a basic vector field v on M such that div Q v ≥ 0 and div Q v > 0 at some point, where div Q is the transverse divergence operator associated to the metric g. Proof. We prove first that the above condition regarding the transverse divergence implies that the foliation is non-taut. coshrmWebarXiv:math/0111270v1 [math.GT] 26 Nov 2001 BOUNDED COCHAINS ON 3–MANIFOLDS DANNY CALEGARI ABSTRACT.In this paper we study the large–scale geometry of 3–manifolds M for which coshrm conference 2022WebCHAPTER 4: FOLIATIONS AND FLOER THEORIES DANNYCALEGARI Abstract. These are notes on the theory of taut foliations on 3-manifolds, which are ... cosh pcabWeb(3) g has negative slope, and M contains taut foliations realizing all boundary slopes in –ÿ1; 1ƒ; in this case, Mb–rƒcontains a taut foliation for all rational r 2–ÿ1; 1ƒ. If Mb–rƒcontains a taut foliation, then Mb–rƒis irreducible [18], has infinite fundamental group [13], and has universal cover R3 [14]. So we have the bread machine rolls allrecipesWebknot in an integer homology 3-sphere admits a co-oriented taut foliation and has left-orderable fundamental group, even if the surgered manifold does not, and that the same … bread machine roll recipeWebA codimension one foliation of is taut if for every leaf of there is a circle transverse to which intersects . Theorem 2.1 (Rummler, Sullivan) . The following conditions are equivalent for transversely orientable … cosh re-entry planWebIndeed, the following fundamental result gives necessary and sufficient conditions for a generalized Finsler structure to be a Finsler structure ([3]): Theorem 2.2 The necessary and sufficient conditions for an (I, J, K)-generalized Finsler struc- ture (Σ, ω) to be realizable as a classical Finsler structure on a surface M are 1. the leaves of the codimension two … bread machine roll dough