The characterization of a line arrangement whose fundamental group of the complement is a direct sum of free groups

Meital Eliyahu; Eran Liberman; Malka Schaps; Mina Teicher

doi:10.2140/agt.2010.10.1285

The characterization of a line arrangement whose fundamental group of the complement is a direct sum of free groups

Meital Eliyahu
, Eran Liberman
, Malka Schaps
, Mina Teicher

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English
Pages (from-to)	1285-1304
Number of pages	20
Journal	Algebraic and Geometric Topology
Volume	10
Issue number	3
DOIs	https://doi.org/10.2140/agt.2010.10.1285
State	Published - 2010

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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.",

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AU - Teicher, Mina

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AB - 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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The characterization of a line arrangement whose fundamental group of the complement is a direct sum of free groups

Abstract

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