Hass, Joel Minimal surfaces in Seifert fiber spaces. (English) Zbl 0559.57005 Topology Appl. 18, 145-151 (1984). Waldhausen showed in 1967 that an embedded 2-sided incompressible surface in a Seifert fiber space can be put in a certain canonical position. It can be made either everywhere transverse to the fibers (horizontal) or everywhere tangent to the fibers (vertical). This paper proves this result with the tools of minimal surface theory. The result proved applies also to non-embedded surfaces and, given a group action, to the equivariant case. Cited in 1 ReviewCited in 3 Documents MSC: 57N10 Topology of general \(3\)-manifolds (MSC2010) 57S17 Finite transformation groups 57R40 Embeddings in differential topology 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) Keywords:equivariant imbeddings; embedded 2-sided incompressible surface in a Seifert fiber space; minimal surface × Cite Format Result Cite Review PDF Full Text: DOI Link References: [1] Epstein, D. B.A., Periodic flows on 3-manifolds, Proc. London Math. Soc., 11, 469-484 (1961) · Zbl 0111.18801 [2] Freedman, M.; Hass, J.; Scott, P., Least area incompressible surfaces in 3-manifolds, Inventiones Math., 71 (1983) · Zbl 0482.53045 [5] Meeks, W. H.; Yau, S. T., The Classical Plateau problem and the topology of 3-dimensional manifolds, Topology, 21, 409-442 (1982) · Zbl 0489.57002 [6] Meeks, W. H.; Simon, L.; Yau, S. T., Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature, Annals of Mathematics, 116, 621-659 (1982) · Zbl 0521.53007 [7] Scott, P., The geometries of 3-manifold, Bull. London Math. Soc., 15, 401-487 (1983) · Zbl 0561.57001 [8] Schoen, R.; Yau, S. T., Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature, Annals of Math., 110, 127-142 (1979) · Zbl 0431.53051 [9] Waldhausen, F., On irreducible 3-manifolds which are sufficiently large, Annals of Math, 87, 56-88 (1968) · Zbl 0157.30603 [10] Waldhausen, F., Eine Klasse von 3-dimensioalen manningfaltigkeiten I, Inventiones Math., 4, 87-117 (1967) 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.