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arxiv: 1207.0584 · v2 · pith:7Z4Z4YTUnew · submitted 2012-07-03 · 🧮 math.GT · math.CO

Realization of intermediate links of line arrangements

classification 🧮 math.GT math.CO
keywords arrangementslinelinkconfigurationsobtainedarrangementseveralsome
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We investigate several topological and combinatorial properties of line arrangements. We associate to a line arrangement a link obtained by intersecting the arrangement with some sphere. Several topics are discussed: (a) some link configurations can be realized by complex line arrangements but not by real line arrangements; (b) if we intersect the arrangements with a vertical band instead of a sphere, what link configurations can be obtained? (c) relations between link configurations obtained by bands and spheres.

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