The structure of subgroup of mapping class groups generated by two Dehn twists (Q1357052)

If \(a\) and \(b\) are simple closed curves on an \(n\)-punctured orientable surface of genus \(g\) then the Dehn twists \(\tau_a\), \(\tau_b\) along \(a\) and \(b\), respectively, generate a subgroup \(H\) of the mapping class group \({\mathcal M}_{g,n}\). The author shows that \(H\) is free if the minimal intersection number of \(a\) and \(b\) is at least 2.