Characterization of Line Arrangement for which the Fundamental Group of the Complement is a Direct Product of Free Groups

摘要

Kwai Man Fan proved that if the intersection lattice of a line arrangementdoes not contain a cycle, then the fundamental group of its complement is adirect sum of infinite and cyclic free groups. He also conjectured that theconverse is true as well. The main purpose of this paper is to prove thisconjecture