Direct product of free groups as the fundamental group of the complement of a union of lines (Q1371320)
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scientific article; zbMATH DE number 1080674
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Direct product of free groups as the fundamental group of the complement of a union of lines |
scientific article; zbMATH DE number 1080674 |
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Direct product of free groups as the fundamental group of the complement of a union of lines (English)
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14 December 1997
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The author defines a topological invariant \(\beta\) of a complex line arrangement (the first Betti number of some associated graph) and proves that in case \(\beta\) vanishes, the fundamental group of the complement of a complex line arrangement is independent of the position of the singularities. Moreover, he proves that for six lines the fundamental group does not depend on the position of the singularities, and gives a counterexample for seven lines.
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fundamental group of the complement of a complex line arrangement
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position of singularities
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