叶理中的嵌布

摘要：

在本文中，我们发现光滑叶理中的光滑嵌入。本文证明了：若流形M的光滑叶理F包含紧致叶L，且H ^1（L;R）= 0，且该叶理是L的某个饱和开邻域U中的乘积叶理，则M上存在C^1-贴近F的叶理F'，且F'有不可数的包含在U中的两两非同胚的螺线管极小集集.如果H^1（L;R）不为0，则已知F的任何足够小的扰动包含饱和乘积邻域。因此，我们的结果可以被认为是一个不稳定性结果，补充了Reeb、Thurston、Langevin和Rosenberg的稳定性结果。

英文摘要：

In this paper we find smooth embeddings of solenoids in smooth foliations. We show that if a smooth foliation F of a manifold M contains a compact leaf L with H^1(L;R)= 0 and if the foliation is a product foliation in some saturated open neighbourhood U of L, then there exists a foliation F' on M which is C^1-close to F, and F' has an uncountable set of solenoidal minimal sets contained in U that are pair wise non-homeomorphic. If H^1(L;R) is not 0, then it is known that any sufficiently small perturbation of F contains a saturated product neighbourhood. Thus, our result can be thought of as an instability result complementing the stability results of Reeb, Thurston and Langevin and Rosenberg.

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