Affordable Access

Closed 1-Forms in Topology and Geometric Group Theory

Authors
  • Farber, Michael
  • Geoghegan, Ross
  • Schuetz, Dirk
Type
Preprint
Publication Date
Oct 06, 2008
Submission Date
Oct 06, 2008
Identifiers
arXiv ID: 0810.0962
Source
arXiv
License
Unknown
External links

Abstract

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.

Report this publication

Statistics

Seen <100 times