Stabilization theorems of Lefschetz fibrations

Nom de l'orateur
Hisaaki Endo (Tokyo)
Etablissement de l'orateur
Tokyo Institute of Technology
Date et heure de l'exposé
Lieu de l'exposé
Salle Eole

In this talk we show two theorems on stabilization of (achiral) Lefschetz fibrations under fiber summing with copies of a `universal' Lefschetz fibration. In particular the first of our stabilization theorems is a generalization of the theorem of Auroux. For proofs of these theorems, we employ a certain labeled finite graph, called a chart, in a closed oriented surface for describing the monodromy of a(n achiral) Lefschetz fibration over the surface. Applying charts and their moves with respect to Wajnryb's presentation of mapping class groups, we generalize a signature formula for Lefschetz fibrations over the 2-sphere obtained by Endo and Nagami to that for Lefschetz fibrations over arbitrary closed oriented surface. This formula is crucial for the proof of the stabilization theorems. This is a joint work with I. Hasegawa, S. Kamada, and K. Tanaka.