Constructing Lefschetz fibrations via Daisy Substitutions

We construct new families of non-hyperelliptic Lefschetz fibrations by applying the daisy substitutions to the families of words $(c_1c_2 \cdots c_{2g-1}c_{2g}{c_{2g+1}}^2c_{2g}c_{2g-1} \cdots c_2c_1)^2 = 1$,$(c_1c_2 \cdots c_{2g}c_{2g+1})^{2g+2} = 1$,and$(c_1c_2 \cdots c_{2g-1}c_{2g})^{2(2g+1)} = 1$inthemappingclassgroup$\Gamma_{g}$ of the closed orientable surface of genus $g$, and study the sections of these Lefschetz fibrations. Furthemore, we show that the total spaces of some of these Lefschetz fibraions are irreducible exotic $4$-manifolds, and compute their Seiberg-Witten invariants. By applying the knot surgery to the family of Lefschetz fibrations obtained from the word $(c_1{c}_2\cdots c_{2g}{c}_{2g+1}{)}^{2g+2}=1$ via daisy substitutions, we also construct an infinite family of pairwise non-diffeomorphic irreducible symplectic and non-symplectic $4$-manifolds homeomorphic to $(g^2 - g + 1){$\mathbb{C}\mathbb{P}$}{}^{2} # (3g^{2} - g(k-3) + 2k + 3)\overline{$\mathbb{C}\mathbb{P}$}{}^{2}$forany$g \geq 3$,and$k = 2, \cdots, g+1$.