Embedding solenoids in foliations

作者：Clark Alex^*; Hurder Steven

来源：Topology and Its Applications, 2011, 158(11): 1249-1270.

DOI：10.1016/j.topol.2011.04.010

• Continuum
• Solenoid
• Foliation
• Embedding

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) not equal to 0 and if the foliation is a product foliation in some saturated open neighborhood 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 pairwise non-homeomorphic. If H(1) (L : R) is 0, then it is known that any sufficiently small perturbation of F contains a saturated product neighborhood. Thus, our result can be thought of as an instability result complementing the stability results of Reeb, Thurston and Langevin and Rosenberg.

• 出版日期2011-7-1