Leaves of Markov local minimal sets in foliations of codimension one
Let M be a compact orientable manifold, and \({\mathcal F}\) a codimension one, transversely orientable \(C^ 2\) foliation of M. An exceptional local minimal set X is said to be Markov if the holonomy pseudogroup of the foliated set (X,\({\mathcal F}| X)\) is generated by a subshift of finite type. The authors prove that if L is an arbitrary leaf of a Markov local minimal set X, then the space of ends of L which are asymptotic to L is homeomorphic to the Cantor set. In the paper there is a proof of the following theorem: Let \(X\subset M\) be a Markov local minimal set of \({\mathcal F}\). Then X contains exactly a countable infinity of resilient leaves. Furthermore, for M 3-dimensional, either \(genus(L)=1\), for each resilient leaf \(L\subset X\), the remaining leaves of \({\mathcal F}| X\) having genus 0, or each leaf \(L\subset X\) has infinite genus and each end asymptotic to L is a cluster point of handles.
scientific article; zbMATH DE number 4153491