|
This article is cited in 9 scientific papers (total in 9 papers)
Closed 1-forms in topology and geometric group theory
M. Farbera, R. Geogheganb, D. Schütza a University of Durham, UK
b State University of New York, Binghamton, USA
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.
Bibliography: 32 titles.
Keywords:
Sigma invariants, Lusternik–Schnirelmann category, Novikov ring, movability of homology classes.
Received: 06.10.2008
Citation:
M. Farber, R. Geoghegan, D. Schütz, “Closed 1-forms in topology and geometric group theory”, Russian Math. Surveys, 65:1 (2010), 143–172
Linking options:
https://www.mathnet.ru/eng/rm9345https://doi.org/10.1070/RM2010v065n01ABEH004663 https://www.mathnet.ru/eng/rm/v65/i1/p145
|
|