Goodman, Sue; Shields, Sandi Modifying a branched surface to carry a foliation. (English) Zbl 1143.57014 Topology Appl. 154, No. 16, 2962-2975 (2007). The authors deal with the problem of existence of transverse foliations for non-singular flows on closed \(3\)-manifolds. They prove for a Reebless flow that it is transverse to a foliation \(F\) if and only if its associated branched transverse surface can be modified to carry \(F\) while staying transverse to the flow. Reviewer: Carlos Arnaldo Morales Rojas (Rio de Janeiro) Cited in 1 ReviewCited in 1 Document MSC: 57R30 Foliations in differential topology; geometric theory 57N10 Topology of general \(3\)-manifolds (MSC2010) 57M50 General geometric structures on low-dimensional manifolds Keywords:branched surface; foliation; transverse flow PDF BibTeX XML Cite \textit{S. Goodman} and \textit{S. Shields}, Topology Appl. 154, No. 16, 2962--2975 (2007; Zbl 1143.57014) Full Text: DOI References: [1] Agol, I.; Li, T., An algorithm to detect laminar 3-manifold, Geom. Topol., 7, 287-309 (2003) · Zbl 1037.57008 [4] Fried, D., Cross sections to a flow, Topology, 21, 265-282 (1982) [5] Gabai, D., Problems in foliations and laminations, (Geometric Topology. Geometric Topology, Athens, Georgia, 1993. Geometric Topology. Geometric Topology, Athens, Georgia, 1993, AMS/IP Stud. Adv. Math., vol. 2.2 (1993)), 1-33 · Zbl 0888.57025 [6] Gabai, D.; Oertel, U., Essential laminations in 3-manifolds, Ann. Math., 130, 41-73 (1989) · Zbl 0685.57007 [7] Goodman, S., Vector fields with transverse foliations, II, Ergodic Theory Dynam. Systems, 6, 193-203 (1986) · Zbl 0606.57012 [8] Milnor, J., On the existence of a connection with curvature zero, Comment. Math. Helv., 32, 215-223 (1958) · Zbl 0196.25101 [9] Naimi, R., Foliations transverse to fibers of Seifert manifolds, Comment. Math. Helv., 69, 155-162 (1994) · Zbl 0797.55009 [10] Novikov, S. P., Topology of foliations, Trudy Moskov. Mat. Obshch.. Trudy Moskov. Mat. Obshch., Trans. Moscow Math. Soc., 14, 268-304 (1967), (in Russian) · Zbl 0247.57006 [11] Schwartzman, S., Asymptotic cycles, Annals of Math., 66, 270-283 (1957) · Zbl 0207.22603 [13] Williams, R. F., Expanding attractors, Inst. Haute Études Sci. Publ. Math., 43, 473-487 (1973) · Zbl 0279.58013 [14] Wood, J., Bundles with totally disconnected structure group, Comment. Math. Helv., 46, 257-273 (1971) · Zbl 0217.49202 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.