Leaf prescriptions for closed 3-manifolds

Cantwell, John; Conlon, Lawrence

doi:10.1090/S0002-9947-1978-0645738-9

Leaf prescriptions for closed $3$-manifolds
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by John Cantwell and Lawrence Conlon PDF

Trans. Amer. Math. Soc. 236 (1978), 239-261 Request permission

Abstract:

Our basic question is: What open, orientable surfaces of finite type occur as leaves with polynomial growth in what closed 3-manifolds? This question is motivated by other work of the authors. It is proven that every such surface so occurs for suitable ${C^\infty }$ foliations of suitable closed 3-manifolds and for suitable ${C^1}$ foliations of all closed 3-manifolds. If the surface has no isolated nonplanar ends it also occurs for suitable ${C^\infty }$ foliations of all closed 3-manifolds. Finally, a large class of surfaces with isolated nonplanar ends occurs in suitable ${C^\infty }$ foliations of all closed, orientable 3-manifolds that are not rational homology spheres.

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Travaux de Novikov sur les feuilletages

Vorlesungen uber Topologie

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