On The CW Complex of the Complement of A Hypersolvable Graphic Arrangement

Abstract

This paper interested in studying a CW complex for the complement of a hypersolvable graphic arrangement that related to a hypersolvable graph , by comparing it with the minimal CW complex for the complement of Jambu's-Papadima's deformed supersolvable arrangement . Motivated by our aim, a dimension of the first non-vanishing higher homotopy group for was calculated and a fashion of the cohomological ring of the complement was considered, just by using the hypersolvable partition analogue on . Moreover, an algorithm to deform any hypersolvable graph into a supersolvable graph was stated. Key-words: connected simple graph, graphic arrangement, hypersolvable (supersolvable) graph, Orlik-Solomon algebra, no broken circuit module, CW complex....