Geodesic
Geometry and topology of ℝ-covered foliations
Calegari, Danny1
1 Department of Mathematics, UC Berkeley, Berkeley, CA 94720
Electronic research announcements of the American Mathematical Society, Tome 06 (2000), pp. 31-39 Cet article a éte moissonné depuis la source American Mathematical Society

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An $\mathbb {R}$-covered foliation is a special type of taut foliation on a $3$-manifold: one for which holonomy is defined for all transversals and all time. The universal cover of a manifold $M$ with such a foliation can be partially compactified by a cylinder at infinity, somewhat analogous to the sphere at infinity of a hyperbolic manifold. The action of $\pi _1(M)$ on this cylinder decomposes into a product by elements of $\text {Homeo}(S^1)\times \text {Homeo}(\mathbb {R})$. The action on the $S^1$ factor of this cylinder is rigid under deformations of the foliation through $\mathbb {R}$-covered foliations. Such a foliation admits a pair of transverse genuine laminations whose complementary regions are solid tori with finitely many boundary leaves, which can be blown down to give a transverse regulating pseudo-Anosov flow. These results all fit in an essential way into Thurston’s program to geometrize manifolds admitting taut foliations.
DOI : 10.1090/S1079-6762-00-00077-9

Calegari, Danny 1

1 Department of Mathematics, UC Berkeley, Berkeley, CA 94720 
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Calegari, Danny. Geometry and topology of ℝ-covered foliations. Electronic research announcements of the American Mathematical Society, Tome 06 (2000), pp. 31-39. doi: 10.1090/S1079-6762-00-00077-9

[1] Calegari, Danny 𝐑-covered foliations of hyperbolic 3-manifolds Geom. Topol. 1999 137 153

[2] Candel, Alberto Uniformization of surface laminations Ann. Sci. École Norm. Sup. (4) 1993 489 516

[3] Gabai, David, Kazez, William H. Homotopy, isotopy and genuine laminations of 3-manifolds 1997 123 138

[4] Gabai, David, Oertel, Ulrich Essential laminations in 3-manifolds Ann. of Math. (2) 1989 41 73

[5] Garnett, Lucy Foliations, the ergodic theorem and Brownian motion J. Functional Analysis 1983 285 311

[6] Novikov, S. P. The topology of foliations Trudy Moskov. Mat. Obšč. 1965 248 278

[7] Sullivan, Dennis A homological characterization of foliations consisting of minimal surfaces Comment. Math. Helv. 1979 218 223

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