Cohomology of surface minimal sets
type: Item
instance of: scholarly article
title: Cohomology of surface minimal sets
zbMATH Open document ID: 0983.37030
author: Konstantin Athanassopoulos
published in: Expositiones Mathematicae
publication date: 2000-04-03T00:00:00Z
review text: The role of minimal sets in the qualitative theory of dynamical systems is known. Here the author proves that the first integral Čech cohomology of a nontrivial surface minimal set is free abelian of rank at least 2. Thus the result on the rank can be considered as an alternative short proof of the more general fact that any 1D continuum \(Y\) carrying a flow without singular points is a periodic orbit if and only if \(\widetilde H^1(Y)\simeq\mathbb{Z}\), where \(\widetilde H^*\) denotes Čech cohomology with integer coefficients.
Mathematics Subject Classification ID: 37C85
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 37B45
Mathematics Subject Classification ID: 37C27
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 1394887
zbMATH Keywords: minimal sets
zbMATH Keywords: Čech cohomology
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1394887