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

Abstract

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

16 pages

Cited by in corpus (2)

• Fundamental groups, Alexander invariants, and cohomology jumping loci
• Line arrangements and direct sums of free groups