الخلاصة

Abstract: Let V be an   dimension vector space over the real or complex numbers. An arrangement A is a finite collection  A M A V H    H of co-dimension one subspaces. Let ( ) be the complement .In this work we use the face poset  (A) of A to construct the homotopy type ofM(A) .More specifically, we would like to know the homotopy properties of M(A)which are relate to various other well-known properties of arrangement ,precisely when M(A) is a K( ,1) -space.