Virtually Free-by-Cyclic Groups

We obtain a homological characterisation of virtually free-by-cyclic groups among groups that are hyperbolic and virtually compact special. As a consequence, we show that many groups known to be coherent actually possess the stronger property of being virtually free-by-cyclic. In particular, we show...

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Bibliographic Details
Published inGeometric and functional analysis Vol. 34; no. 5; pp. 1580 - 1608
Main Authors Kielak, Dawid, Linton, Marco
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2024
Springer Nature B.V
Subjects
Analysis
Mathematics
Mathematics and Statistics
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Summary:We obtain a homological characterisation of virtually free-by-cyclic groups among groups that are hyperbolic and virtually compact special. As a consequence, we show that many groups known to be coherent actually possess the stronger property of being virtually free-by-cyclic. In particular, we show that all one-relator groups with torsion are virtually free-by-cyclic, solving a conjecture of Baumslag.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-024-00687-6