Some results related to finiteness properties of groups for families of subgroups

Von Puttkamer T, Wu X (2020)
Algebraic & Geometric Topology 20(6): 2885-2904.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Von Puttkamer, Timm; Wu, XiaoleiUniBi
Abstract / Bemerkung
Let (E)double-under-barG be the classifying space of G for the family of virtually cyclic subgroups. We show that an Artin group admits a finite model for (E)double-under-barG if and only if it is virtually cyclic. This solves a conjecture of Juan-Pineda and Leary and a question of Luck, Reich, Rognes and Varisco for Artin groups. We then study conjugacy growth of CAT(0) groups and show that if a CAT(0) group contains a free abelian group of rank two, its conjugacy growth is strictly faster than linear. This also yields an alternative proof for the fact that a CAT(0) cube group admits a finite model for (E)double-under-barG if and only if it is virtually cyclic. Our last result deals with the homotopy type of the quotient space (B)double-under-barG = (E)double-under-barG/G. We show, for a poly-Z -group G, that (B)double-under-barG is homotopy equivalent to a finite CW-complex if and only if G is cyclic.
Erscheinungsjahr
2020
Zeitschriftentitel
Algebraic & Geometric Topology
Band
20
Ausgabe
6
Seite(n)
2885-2904
eISSN
1472-2739
Page URI
https://pub.uni-bielefeld.de/record/2950255

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Von Puttkamer T, Wu X. Some results related to finiteness properties of groups for families of subgroups. Algebraic & Geometric Topology. 2020;20(6):2885-2904.
Von Puttkamer, T., & Wu, X. (2020). Some results related to finiteness properties of groups for families of subgroups. Algebraic & Geometric Topology, 20(6), 2885-2904. doi:10.2140/agt.2020.20.2885
Von Puttkamer, T., and Wu, X. (2020). Some results related to finiteness properties of groups for families of subgroups. Algebraic & Geometric Topology 20, 2885-2904.
Von Puttkamer, T., & Wu, X., 2020. Some results related to finiteness properties of groups for families of subgroups. Algebraic & Geometric Topology, 20(6), p 2885-2904.
T. Von Puttkamer and X. Wu, “Some results related to finiteness properties of groups for families of subgroups”, Algebraic & Geometric Topology, vol. 20, 2020, pp. 2885-2904.
Von Puttkamer, T., Wu, X.: Some results related to finiteness properties of groups for families of subgroups. Algebraic & Geometric Topology. 20, 2885-2904 (2020).
Von Puttkamer, Timm, and Wu, Xiaolei. “Some results related to finiteness properties of groups for families of subgroups”. Algebraic & Geometric Topology 20.6 (2020): 2885-2904.

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