Poly-freeness of Artin groups and the Farrell-Jones Conjecture

Wu X (2022)
Journal of Group Theory 25(1): 11-24.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We provide two simple proofs of the fact that even Artin groups of FC-type are poly-free which was recently established by R. Blasco-Garcia, C. Martinez-Perez and L. Paris. More generally, let Gamma be a finite simplicial graph with all edges labelled by positive even integers, and let A(Gamma) be its associated Artin group; our new proof implies that if A(T) is poly-free (resp. normally poly-free) for every clique T in Gamma, then A(Gamma) is poly-free (resp. normally poly-free). We prove similar results regarding the Farrell-Jones Conjecture for even Artin groups. In particular, we show that if A(Gamma) is an even Artin group such that each clique in Gamma either has at most three vertices, has all of its labels at least 6, or is the join of these two types of cliques (the edges connecting the cliques are all labelled by 2), then A(Gamma) satisfies the Farrell-Jones Conjecture. In addition, our methods enable us to obtain results for general Artin groups.
Erscheinungsjahr
2022
Zeitschriftentitel
Journal of Group Theory
Band
25
Ausgabe
1
Seite(n)
11-24
ISSN
1433-5883
eISSN
1435-4446
Page URI
https://pub.uni-bielefeld.de/record/2960716

Zitieren

Wu X. Poly-freeness of Artin groups and the Farrell-Jones Conjecture. Journal of Group Theory . 2022;25(1):11-24.
Wu, X. (2022). Poly-freeness of Artin groups and the Farrell-Jones Conjecture. Journal of Group Theory , 25(1), 11-24. https://doi.org/10.1515/jgth-2020-0201
Wu, X. (2022). Poly-freeness of Artin groups and the Farrell-Jones Conjecture. Journal of Group Theory 25, 11-24.
Wu, X., 2022. Poly-freeness of Artin groups and the Farrell-Jones Conjecture. Journal of Group Theory , 25(1), p 11-24.
X. Wu, “Poly-freeness of Artin groups and the Farrell-Jones Conjecture”, Journal of Group Theory , vol. 25, 2022, pp. 11-24.
Wu, X.: Poly-freeness of Artin groups and the Farrell-Jones Conjecture. Journal of Group Theory . 25, 11-24 (2022).
Wu, Xiaolei. “Poly-freeness of Artin groups and the Farrell-Jones Conjecture”. Journal of Group Theory 25.1 (2022): 11-24.

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