Closed 1-forms in topology and geometric group theory
Closed 1-forms in topology and geometric group theory
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拓扑和几何群论中的闭 1-形式
DOI：
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发表时间：
2008
期刊：
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通讯作者：
Dirk Schuetz
中科院分区：
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作者：
Michael Farber;R. Geoghegan;Dirk Schuetz
In this article we describe relations of the topology of closed 1-forms to the group-theoretic invariants of Bieri-Neumann-Strebel-Renz. Starting with a survey, we extend these Sigma invariants to finite CW-complexes and show that many properties of the group-theoretic version have analogous statements. In particular, we show the relation between Sigma invariants and finiteness properties of certain infinite covering spaces. We also discuss applications of these invariants to the Lusternik-Schnirelmann category of a closed 1-form and to the existence of a non-singular closed 1-form in a given cohomology class on a high-dimensional closed manifold.
