Closed 1-Forms in Topology and Geometric Group Theory

Details Closed 1-Forms in Topology and Geometric Group Theory Closed 1-Forms in Topology and Geometric Group Theory

2008-10-06

arxiv.org/abs/0810.0962v1

Mathematics

Algebraic Topology

32 pages

Scientific paper

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.

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