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Russian Mathematical Surveys, 2010, Volume 65, Issue 1, Pages 143–172
DOI: https://doi.org/10.1070/RM2010v065n01ABEH004663 (Mi rm9345) 		 
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
English version PDF (574 kB) Citations (9)
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DOI: https://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.
Bibliography: 32 titles.
Keywords: Sigma invariants, Lusternik–Schnirelmann category, Novikov ring, movability of homology classes.
Received: 06.10.2008
Russian version:
Uspekhi Matematicheskikh Nauk, 2010, Volume 65, Issue 1(391), Pages 145–176
DOI: https://doi.org/10.4213/rm9345
Bibliographic databases:
Document Type: Article
UDC: 515.165
MSC: Primary 20J05, 58E05; Secondary 55M30
Language: English
Original paper language: Russian
Citation: M. Farber, R. Geoghegan, D. Schütz, “Closed 1-forms in topology and geometric group theory”, Uspekhi Mat. Nauk, 65:1(391) (2010), 145–176; Russian Math. Surveys, 65:1 (2010), 143–172
Citation in format AMSBIB
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\paper Closed 1-forms in topology and geometric group theory
\jour Uspekhi Mat. Nauk
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\vol 65
\issue 1(391)
\pages 145--176
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:46
    First page:13
     
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