Symplectic surgeries along certain singularities and new Lefschetz fibrations

We define a new 4-dimensional symplectic cut and paste operations arising from the generalized star relations (t_a0 t_a1 t_a2 ⋯t_a2g+1 )^2g+1=t_b1 t_b2 ^gt_b3 , also known as the trident relations, in the mapping class group Γ_g,3 of an orientable surface of genus g≥1 with 3 boundary components. We also construct new families of Lefschetz fibrations by applying the (generalized) star relations and the chain relations to the families of words (t_c1 t_c2 ⋯t_c2g−1 t_c2g t_c2g+1 ²t_c2g t_c2g−1 ⋯t_c2 t_c1 )²ⁿ=1, (t_c1 t_c2 ⋯t_c2g t_c2g+1 )^(2g+2)n=1 and (t_c1 t_c2 ⋯t_c2g−1 t_c2g )^2(2g+1)n=1 in the mapping class group Γ_g of the closed orientable surface of genus g≥1 and n≥1. Furthermore, we show that the total spaces of some of these Lefschetz fibrations are irreducible exotic symplectic 4-manifolds. Using the degenerate cases of the generalized star relations, we also realize all elliptic Lefschetz fibrations and genus two Lefschetz fibrations over S² with non-separating vanishing cycles.