Taut foliation
WebFirst constructed by Meigniez, these foliations occupy an intermediate position between ℝ-covered foliations and arbitrary taut foliations of 3-manifolds. We show that for a taut foliation F with one-sided branching of an atoroidal 3-manifold M, one can construct a pair of genuine laminations Λ ± of M transverse to F with solid torus ... WebCHAPTER 4: FOLIATIONS AND FLOER THEORIES DANNYCALEGARI Abstract. These are notes on the theory of taut foliations on 3-manifolds, which are ...
Taut foliation
Did you know?
In mathematics, tautness is a rigidity property of foliations. A taut foliation is a codimension 1 foliation of a closed manifold with the property that every leaf meets a transverse circle. By transverse circle, is meant a closed loop that is always transverse to the tangent field of the foliation. If … See more Taut foliations are closely related to the concept of Reebless foliation. A taut foliation cannot have a Reeb component, since the component would act like a "dead-end" from which a transverse curve could never escape; … See more The existence of a taut foliation implies various useful properties about a closed 3-manifold. For example, a closed, orientable 3 … See more By a theorem of Hansklaus Rummler and Dennis Sullivan, the following conditions are equivalent for transversely orientable codimension one foliations $${\displaystyle \left(M,{\mathcal {F}}\right)}$$ of closed, orientable, smooth manifolds M: See more http://www.map.mpim-bonn.mpg.de/Foliation
Webcodimension-1 foliation of M meeting ¶M transversely, then F is said to be taut if each leaf of F intersects a closed transversal to F. For example, if a transversely oriented foliation has only non-compact leaves, then it is necessarily taut [9]. A lamination is a codimension-1 foliation of a closed subset of M meeting ¶M transversely. 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
WebProperties of manifolds with taut foliation Question What are the topological/geometric consequences of having a taut foliation? Theorem (Palmeira, Rosenberg, Hae iger) If M is a closed, orientable 3-manifold that has a taut foliation with no sphere leaves then M is covered by R3, M is irreducible and has in nite fundamental group. Theorem ... WebA codimension one foliation on a closed three-manifold is taut if the manifold has a closed 2-form inducing an area form on each leaf of the foliation.Equivalently, by a theorem of Sullivan [], the foliation is taut if, through every point, there is a loop everywhere transverse to the leaves.This characterization shows that a taut foliation does not contain any Reeb …
Web(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
WebIn mathematics, tautness is a rigidity property of foliations. A taut foliation is a codimension 1 foliation of a closed manifold with the property that every leaf meets a transverse … fons and porter videosfonsas next action 3.4.1http://geometrie.math.cnrs.fr/Calegari3.pdf eileen fisher sheer topWebIII. CTFs. Taut foliation de nition De nition (taut foliation). A codimension-1 foliation Fon a closed oriented 3-manifold M is called taut if for every x 2M, there is a closed transversal … fons and porter\u0027s love of quilting magazineWebL-spaces, taut foliations, and graph manifolds - Volume 156 Issue 3 Due to planned system work, ecommerce on Cambridge Core will be unavailable on 12 March 2024 from 08:00 – … eileen fisher sheer linen shower curtainWebThe 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. fonsas next action weakauraWebIndeed, 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 … fons aseraクリニック