Systolic invariants of groups and 2-complexes via Grushko decomposition

2006/09/14 by Yuli B. Rudyak, Rudyak, Yuli B., Stéphane Sabourau +1 · 1 citation
Mathematics · #53C23 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0609379

openalex publication_date 2006/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a finiteness result for the systolic area of groups, answering a question of M. Gromov. Namely, we show that there are only finitely many possible unfree factors of fundamental groups of~2-complexes whose systolic area is uniformly bounded. 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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