## 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.## References

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## Additional Information

- © Copyright 1978 American Mathematical Society
- 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