Foliation dynamics and leaf invariants
type: Item
instance of: scholarly article
title: Foliation dynamics and leaf invariants
zbMATH Open document ID: 0604.57021
DOI: 10.1007/BF02567418
published in: Commentarii Mathematici Helvetici
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/140017
review text: The author studies the relationship of leaf invariants of a foliation with the growth type of leaves. Leaf invariants are the characteristic classes of the normal bundles of the foliation restricted to a leaf, where the bundle is considered as a flat bundle. The main result in this direction is Theorem 3. Let L be a leaf of a \(C^ 2\)-foliation \({\mathcal F}\). If there is a leaf invariant \(y\in H^ m(L)\) with \(m>1\) and \(y\neq 0\), then the linear holonomy group of L is not amenable. The non-amenability of the linear holonomy group of L is related to the growth types of leaves of the foliation via Theorem 1. If the linear holonomy group of L is not amenable, then there is a leaf L' in the closure of L such that for any Riemannian metric on the foliated manifold L' has exponential growth.
reviewed by: Elmar Vogt
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 37A99
Mathematics Subject Classification ID: 58H05
Mathematics Subject Classification ID: 43A07
zbMATH DE Number: 3975899
zbMATH Keywords: leaf invariants of a foliation
zbMATH Keywords: growth type of leaves
zbMATH Keywords: characteristic classes
zbMATH Keywords: linear holonomy group
zbMATH Keywords: amenable
zbMATH Keywords: exponential growth
author: Steven Hurder
MaRDI profile type: Publication
OpenAlex ID: W1997108421
description: scientific article; zbMATH DE number 3975899