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Closed 1-forms in topology and geometric group theory
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Farber, Michael, Geoghegan, Ross and Schutz, Dirk (2010) Closed 1-forms in topology and geometric group theory. Russian Mathematical Surveys, Vol.65 (No.1). pp. 143-172. doi:10.1070/RM2010v065n01ABEH004663 ISSN 0036-0279.
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Official URL: http://dx.doi.org/10.1070/RM2010v065n01ABEH004663
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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Russian Mathematical Surveys | ||||
Publisher: | Turpion Ltd. | ||||
ISSN: | 0036-0279 | ||||
Official Date: | 2010 | ||||
Dates: |
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Volume: | Vol.65 | ||||
Number: | No.1 | ||||
Page Range: | pp. 143-172 | ||||
DOI: | 10.1070/RM2010v065n01ABEH004663 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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