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

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

2008-10-30

arxiv.org/abs/0810.5533v3

Mathematics

Algebraic Topology

16 pages

Scientific paper

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

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