2019/07/02 by Eugenio Borghini, Borghini, Eugenio, Elías Gabriel Minian +2
Mathematics · #53C23 #57M20 #57N16 #57Q15 #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT #msc:53C23 #msc:57M20 #msc:57N16 #msc:57Q15
paper · pdf · doi:10.48550/arxiv.1907.01667
9 pages
arxiv created 2019/07/02 · openalex publication_date 2019/07/02 · arxiv updated 2019/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The simplicial complexity is an invariant for finitely presentable groups that was recently introduced by Babenko, Balacheff and Bulteau to study systolic area. The simplicial complexity κ(G) was proved to be a good approximation of the systolic area σ(G) for large values of κ(G). In this paper we compute the simplicial complexity of all surface groups (both in the orientable and in the non-orientable case). This settles a problem raised by Babenko, Balacheff and Bulteau. We also prove that κ(G∗ ℤ)=κ(G) for any surface group G. This provides the first partial evidence in favor of the conjecture of the stability of the simplicial complexity under free product with free groups. The general stability problem, both for simplicial complexity and for systolic area, remains open.