Lefschetz fibrations with arbitrary signature

Spin Lefschetz fibrations are abundant

“…We begin with a review of the concepts and background results underlying the rest of our article, along with our conventions. We refer the reader to [10] for more details and comprehensive references on Lefschetz fibrations, symplectic 4-manifolds, and monodromy factorizations, and to [3] for their interplay with spin structures.…”

“…Hence all the monodromy curves of X P g satisfy the spin condition, which is all we needed at this point. 3 To sum up, we have the following:…”

“…Brown curves indicate where the boundary curves {δ i } of 4 2 in the positive factorization ( 6) are mapped to. Blue arrows illustrate how we isotope the boundaries of 4 2 ⊂ ‫ޒ‬ 3 before embedding it into g ⊂ ‫ޒ‬ 3 . Red curves constitute a geometric generating set for H 1 ( g ; ‫ޚ‬ 2 ).…”

“…Here we adopted Korkmaz's generating set to make our calculations comparable to his work in[14], which yields a nonstandard expression for the surface relator as iterated conjugates, resulting in C g = 1.2 It may be worth noting that this is not a trial and error process. By the heuristic arguments of[3], we are proceeding with an educated guess, since these fibrations are known to come from pencils on the spin manifolds S 2 × n ; see[11].…”