On the intersection form of fillings

Abstract

We prove, by an ad hoc method, that topologically simple exact fillings of flexibly fillable contact manifolds with vanishing first Chern class have unique integral intersection forms and discuss cases where the topologically simple assumption can be removed. We appeal to the special Reeb dynamics (stronger than ADC in [13]) on the contact boundary, while a more systematic approach working for general ADC manifolds is developed independently by Eliashberg, Ganatra and Lazarev [9].