A topological interpretation for vanishing of higher homotopy groups of a hypersolvable arrangements

Abstract EN

In this paper we constructed a minimal CW complex for the complement of a Super solvable arrangement induced from the structure of its fundamental group as iterated semi direct product of finitely generated groups, in order to give a topological interpretation for vanishing of higher homotopy groups of the complement of a hypersolvable r –arrangement A , when we deformed it by Jambu's and Papadima's deformation method into a one parameter family of fiber-type arrangements {At}t € C.