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Yuli B. Rudyak; Stéphane Sabourau
Systolic invariants of groups and $2$-complexes via Grushko decomposition
(Invariants systoliques des groupes et $2$-complexes via la décomposition de Grushko)
Annales de l'institut Fourier, 58 no. 3 (2008), p. 777-800, doi: 10.5802/aif.2369
Article PDF | Reviews MR 2427510 | Zbl 1142.53035 | 1 citation in Cedram
Class. Math.: 53C23, 20E06
Keywords: Systole, systolic area, systolic ratio, $2$-complex, Grushko decomposition

Résumé - Abstract

We prove a finiteness result for the systolic area of groups. Namely, we show that there are only finitely many possible unfree factors of fundamental groups of $2$-complexes whose systolic area is uniformly bounded. We also show that the number of freely indecomposable such groups grows at least exponentially with the bound on the systolic area. Furthermore, we prove a uniform systolic inequality for all $2$-complexes with unfree fundamental group that improves the previously known bounds in this dimension.

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