THE HIGHER TOPOLOGICAL COMPLEXITY OF A COMPLEMENT OF COMPLEX LINES ARRANGEMENT

Abstract

The complement of complex lines arrangement in C² is a smooth manifold with many geometric
properties v  interested in studying the theory of the hyperplanes arrangement. Some geometric
invariants of this manifold are combinatorial dependence, meaning they depend only on the set
of intersections of lines. In this paper, we calculate the high topological complexity of the complement of the center complex lines arrangement in C² and show the combinatorial dependence of this geometric invariant.