Constructing Lefschetz fibrations via daisy substitutions

Abstract

We construct new families of nonhyperelliptic Lefschetz fibrations by applying the daisy substitutions to the families of words (c1c2 ⋯ c2g-1c2gc2g+12c2g · c2g-1 ⋯ c2c1)2 = 1, (c1c2 ⋯ c2gc2g+1)2g+2 = 1, and (c1c2 ⋯ c2g-1c2g)2(2g+1) = 1 in themapping class group Γg of the closed orientable surface of genus g, and we study the sections of theseLefschetz fibrations. Furthermore, we show that the total spaces of some of these Lefschetz fibrations are irreducible exotic 4-manifolds, and we compute their Seiberg-Witten invariants. By applying the knot surgery to the family of Lefschetz fibrations obtained from the word (c1c2 ⋯ c2gc2g+1)2g+2 = 1 via daisy substitutions, we also construct an infinite family of pairwise nondiffeomorphic irreducible symplectic and nonsymplectic 4-manifolds homeomorphic to (g2 - g + 1)ℂℙ2#(3g2 - g(k - 3) + 2k +3)ℂℙ2 for any g ≥ 3 and k = 2, ⋯, g + 1.