2023/07/26 by Kumar, Rakesh
#05C10 (Secondary) #57K20 #57M15 (Primary) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2307.13970
Let Sg denote a closed oriented surface of genus g ≥ 2. A set Ω= \ c1, …, cd\ of pairwise non-homotopic simple closed curves on Sg is called a filling system or simply a filling of Sg, if Sg∖ Ω is a union of ℓ topological discs for some ℓ≥ 1. For 1≤ i≤ d, let Tci denotes the Dehn twist along ci. In this article, we show that for each d≥ 2, there exists a filling Ω=\c1,c2,…, cd\ of Sg such that the group ⟨ Tc1, Tc2,…,Tcd⟩ is isomorphic to the free group of rank d.