Global cross sections and minimal flows
type: Item
instance of: scholarly article
title: Global cross sections and minimal flows
zbMATH Open document ID: 1016.37011
DOI: 10.1016/S0166-8641(01)00094-3
published in: Topology and its Applications
publication date: 2002-08-22T00:00:00Z
review text: This interesting work studies the fine structure of flows with a global cross section that is a closed disk. It is assumed that the first return map is a cellular map, which is here defined as a map bijective on the ambient space, continuous on open cells, and such that the image of any open cell is an open cell. Mind that it is not generally continuous. Geometrically important is the induced branched manifold, essentially a cross section with the one-sided trace of its boundary. It is contractible if and only if the flow lives on a homotopy sphere. Elaborate examples are constructed in dimension 3.
reviewed by: Dieter Erle
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 37B05
Mathematics Subject Classification ID: 37B35
Mathematics Subject Classification ID: 57N12
zbMATH DE Number: 1787536
zbMATH Keywords: suspension
zbMATH Keywords: first return map
zbMATH Keywords: cellular map
zbMATH Keywords: branched manifold
zbMATH Keywords: examples
Wikidata QID: Q57441642
author: William F. Basener
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1787536