THE KAROUBI-WEIBEL COMPLEXITY FOR GROUPS
Résumé
Let G be a finitely presented group. A new complexity called Karoubi-Weibel complexity or covering type, is defined for G. The construction is inspired by recent work of Karoubi and Weibel [16], initially applied to topological spaces. We introduce a similar notion in combinatorial form in order to apply it to finitely presentable groups. Some properties of this complexity as well as a few examples of calculation/estimation for certain classes of finitely presentable groups are considered. Finally we give a few applications of complexity to some geometric problems, namely to the systolic area and the volume entropy of groups.
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Est une version de hal-05077453 Article Ivan Babenko, Thiziri Moulla. The Karoubi-Weibel complexity for groups. L'Enseignement Mathématique , 2024, 70 (1), pp.197-230. ⟨10.4171/LEM/1041⟩. ⟨hal-05077453⟩