zbMATH — the first resource for mathematics

Riemann surface laminations. (Laminations par surfaces de Riemann.) (French) Zbl 1018.37028
Cerveau, Dominique et al., Dynamique et géométrie complexes. Paris: Société Mathématique de France. Panor. Synth. 8, 49-95 (1999).
This very well-written paper contains a systematic analysis of the properties of laminations by Riemann surfaces. Roughly speaking, a lamination is a generalization of a foliation to compact spaces which are not manifolds. The paper begins with a series of examples, e.g. the construction by Sullivan of a lamination associated to a \(\mathbb{C}^r\) expanding map of the circle. Differential forms on a lamination are constructed in Section 3; then Section 4 is devoted to a Riemann-Roch formula for a lamination. Section 5 and 6 treat the problem of uniformization of a lamination. The last paragraph, Section 7, give three theorems on the existence of non-constant meromorphic functions on a lamination.
For the entire collection see [Zbl 1010.00008].

37F75 Dynamical aspects of holomorphic foliations and vector fields
30F10 Compact Riemann surfaces and uniformization
57R30 Foliations in differential topology; geometric theory
57M50 General geometric structures on low-dimensional manifolds
Full Text: Link