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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Leaf prescriptions for closed $ 3$-manifolds


Authors: John Cantwell and Lawrence Conlon
Journal: Trans. Amer. Math. Soc. 236 (1978), 239-261
MSC: Primary 57D30
DOI: https://doi.org/10.1090/S0002-9947-1978-0645738-9
MathSciNet review: 0645738
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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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DOI: https://doi.org/10.1090/S0002-9947-1978-0645738-9
Article copyright: © Copyright 1978 American Mathematical Society