Geodesic
A sufficient condition for a branched surface to fully carry a lamination
Zannad, Skander1
1Laboratoire Jean Leray, 2 rue de la Houssinière, BP 92208, 44322 Nantes Cedex 03, France
Algebraic and Geometric Topology, Tome 7 (2007) no. 3, pp. 1599-1632
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We give a sufficient condition for a branched surface in a 3 dimensional manifold to fully carry a lamination, giving a piece of answer to a classical question of D Gabai.

DOI : 10.2140/agt.2007.7.1599
Keywords: branched surface, lamination, twisted curve

Zannad, Skander  1

1 Laboratoire Jean Leray, 2 rue de la Houssinière, BP 92208, 44322 Nantes Cedex 03, France 
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Zannad, Skander. A sufficient condition for a branched surface to fully carry a lamination. Algebraic and Geometric Topology, Tome 7 (2007) no. 3, pp. 1599-1632. doi: 10.2140/agt.2007.7.1599

[1] J Christy, Immersing branched surfaces in dimension three, Proc. Amer. Math. Soc. 115 (1992) 853

[2] D Gabai, Problems in foliations and laminations, from: "Geometric topology (Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 1

[3] D Gabai, U Oertel, Essential laminations in $3$–manifolds, Ann. of Math. $(2)$ 130 (1989) 41

[4] T Li, Laminar branched surfaces in $3$–manifolds, Geom. Topol. 6 (2002) 153

[5] L Mosher, U Oertel, Spaces which are not negatively curved, Comm. Anal. Geom. 6 (1998) 67

[6] U Oertel, J Światkowski, Contact Structures, $\sigma$–Confoliations and Contaminations in $3$–manifolds (2003)

[7] U Oertel, J Światkowski, A contamination carrying criterion for branched surfaces (2003)

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