Foliated control with hyperbolic leaves
type: Item
instance of: scholarly article
title: Foliated control with hyperbolic leaves
zbMATH Open document ID: 0658.57020
DOI: 10.1007/BF00539622
published in: \(K\)-Theory
publication date: 1987-01-01T00:00:00Z
review text: The main result is a control theorem for the space of stable pseudo- isotopies on E with control near the leaves of F in M, where \(\rho\) : \(E\to M\) is a fiber bundle over the compact closed Riemannian manifold M having a compact manifold for fiber and F is a smooth foliation of M. The proof of this foliated control result combines the (unfoliated) control results of \textit{F. Quinn} [Invent. Math. 68, 353-424 (1982; Zbl 0533.57008)] with the `long and thin' cell structures and the `asymptotic transfer' of the authors' papers: ``K-theory and dynamics. I, II'' [Ann. Math., II. Ser. 124, 531-569 (1986; Zbl 0653.58035) and ibid. 126, 451- 493 (1987)].
Mathematics Subject Classification ID: 57R52
Mathematics Subject Classification ID: 57Q60
Mathematics Subject Classification ID: 57N15
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 4076086
zbMATH Keywords: control near leaves
zbMATH Keywords: controlled isotopies
zbMATH Keywords: hyperbolic leaves
zbMATH Keywords: space of stable pseudo-isotopies
zbMATH Keywords: fiber bundle
zbMATH Keywords: smooth foliation
zbMATH Keywords: foliated control
zbMATH Keywords: `long and thin' cell structures
zbMATH Keywords: asymptotic transfer
author: F. Thomas Farrell
author: Lowell Jones
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00539622
OpenAlex ID: W2016789204
description: scientific article; zbMATH DE number 4076086