abstract: Several types of minimal presentations of π1 for arrangements complements have been known since long time. More generally, arrangements complements are known to be homotopy equivalent to minimal CW complex. In this talk, we focus on two dimensional complexified real arrangements and introduce “minimal stratification” which can be considered as a dual notion to minimal CW complex. As applications, we will give a new minimal positive homogeneous presentation for the fundamental group, and discuss how to recover local system cohomology groups from the Aomoto complex.
Yoshinaga - Minimal Stratification