2009/01/31 by Justin Malestein, Andrew Putman
Mathematics · #Algebraic Geometry and Number Theory #Central series #Combinatorics #Differential geometry #Element (criminal law) #Free group #Fundamental group #Geometric and Algebraic Topology #Geometry #Group (periodic table) #Hyperbolic geometry #Mathematical Dynamics and Fractals #Mathematics #Nilpotent #Nilpotent group #Projective geometry #Pure mathematics #Series (stratigraphy) #Surface (topology) #Topological group #Topology (electrical circuits) #math.GR #math.GT
paper · pdf · doi:10.1007/s10711-010-9465-z
published as Geom. Dedicata. 149 (2010), no. 1, 73-84 · 13 pages, 3 figures; a few corrections; to appear in Geom. Dedicata
openalex publication_date 2010/01/27 · arxiv created 2013/03/13 · arxiv updated 2020/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We give various estimates of the minimal number of self-intersections of a nontrivial element of the kth term of the lower central series and derived series of the fundamental group of a surface. As an application, we obtain a new topological proof of the fact that free groups and fundamental groups of closed surfaces are residually nilpotent. Along the way, we prove that a nontrivial element of the kth term of the lower central series of a nonabelian free group has to have word length at least k in a free generating set.