Agrarian and L-2-invariants

Henneke F, Kielak D (2021)
Fundamenta Mathematicae .

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Henneke, Fabian; Kielak, DawidUniBi
Abstract / Bemerkung
We develop the theory of agrarian invariants, which are algebraic coun-terparts to L-2-invariants. Specifically, we introduce the notions of agrarian Betti numbers, agrarian acyclicity, agrarian torsion and agrarian polytope for finite free G-CW-complexes together with a fixed choice of a ring homomorphism from the group ring ZG to a skew field. For the particular choice of the Linnell skew field D(G), this approach recovers most of the information encoded in the corresponding L-2-invariants. As an application, we prove that for agrarian groups of deficiency 1, the agrarian poly-tope admits a marking of its vertices which controls the Bieri-Neumann-Strebel invariant of the group, improving a result of the second author and partially answering a question of Friedl-Tillmann. We also use the technology developed here to prove the Friedl-Tillmann conjecture on polytopes for two-generator one-relator groups; the proof forms the content of another article.
Stichworte
agrarian invariants; L-2-invariants
Erscheinungsjahr
2021
Zeitschriftentitel
Fundamenta Mathematicae
ISSN
0016-2736
eISSN
1730-6329
Page URI
https://pub.uni-bielefeld.de/record/2957748

Zitieren

Henneke F, Kielak D. Agrarian and L-2-invariants. Fundamenta Mathematicae . 2021.
Henneke, F., & Kielak, D. (2021). Agrarian and L-2-invariants. Fundamenta Mathematicae . https://doi.org/10.4064/fm808-4-2021
Henneke, F., and Kielak, D. (2021). Agrarian and L-2-invariants. Fundamenta Mathematicae .
Henneke, F., & Kielak, D., 2021. Agrarian and L-2-invariants. Fundamenta Mathematicae .
F. Henneke and D. Kielak, “Agrarian and L-2-invariants”, Fundamenta Mathematicae , 2021.
Henneke, F., Kielak, D.: Agrarian and L-2-invariants. Fundamenta Mathematicae . (2021).
Henneke, Fabian, and Kielak, Dawid. “Agrarian and L-2-invariants”. Fundamenta Mathematicae (2021).

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