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Proceedings of the American Mathematical Society

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Groups acting on trees and the Eilenberg-Ganea problem for families


Author: Luis Jorge Sánchez Saldaña
Journal: Proc. Amer. Math. Soc. 148 (2020), 5469-5479
MSC (2010): Primary 57M20, 20J05; Secondary 55N25
DOI: https://doi.org/10.1090/proc/15203
Published electronically: August 17, 2020
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Abstract: We construct new examples of groups with cohomological dimension 2 and geometric dimension 3 with respect to the families of finite subgroups, virtually abelian groups of bounded rank, and the family of virtually poly-cyclic subgroups. Our main ingredients are the examples constructed by Brady-Leary-Nucinckis and Fluch-Leary, and Bass-Serre theory.


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Luis Jorge Sánchez Saldaña
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior S/N, Cd. Universitaria, Colonia Copilco el Bajo, Delegación Coyoacán, 04510, México D.F., Mexico
Email: luisjorge@ciencias.unam.mx

DOI: https://doi.org/10.1090/proc/15203
Received by editor(s): November 6, 2019
Received by editor(s) in revised form: May 15, 2020, and May 21, 2020
Published electronically: August 17, 2020
Additional Notes: This work was funded by the Mexican Council of Science and Technology via the program Estancias postdoctorales en el extranjero, and by the NSF via grant DMS-1812028.
Communicated by: David Futer
Article copyright: © Copyright 2020 American Mathematical Society