Every surface is a leaf
type: Item
instance of: scholarly article
title: Every surface is a leaf
zbMATH Open document ID: 0621.57014
DOI: 10.1016/0040-9383(87)90001-2
author: John Cantwell
author: Lawrence Conlon
published in: Topology
publication date: 1987-01-01T00:00:00Z
review text: Let L denote an open, connected 2-manifold, M a closed, connected 3- manifold. The main theorem of the paper asserts that if L is orientable and M is arbitrary, or if L and M are both nonorientable, then there exists a transversely orientable, \(C^{\infty}\) foliation of M having a leaf diffeomorphic to L. Directly from the construction in the proof of this theorem the authors obtain the following results: (1) Every open surface can be realized as a leaf with exponential growth in suitable closed, \(C^{\infty}\)-foliated 3-manifolds. (2) There exists a transversely orientable, \(C^{\infty}\) foliation of M and a Riemannian metric on M such that a certain leaf \(L_*\) lies at infinite level, is diffeomorphic to L, and has constant curvature -1. The authors also assert that the assumption of compactness of M in the main theorem can be omitted.
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 53C12
zbMATH DE Number: 4007265
zbMATH Keywords: foliation of 3-manifold
zbMATH Keywords: hyperbolic leaf
zbMATH Keywords: foliation of codimension 1
zbMATH Keywords: realizing a 2-manifold as a leaf
zbMATH Keywords: leaf with exponential growth
zbMATH Keywords: foliated 3-manifolds
zbMATH Keywords: infinite level
MaRDI profile type: Publication
full work available at URL: 0040-9383(87)90001-2
OpenAlex ID: W2085604550
description: scientific article; zbMATH DE number 4007265