THE HIGHER TOPOLOGICAL COMPLEXITY OF GENERIC ARRANGEMENT

Abstract

The higher topological complexity is given by Y.B. Rudyak introduced in 2010 as a topological invariant that has many relations with other invariants. It is difficult to compute this invariant in the general case. In this paper, we give the results of higher topological complexity for the complement of generic arrangement in complex space. To get this result, we give the upper bound by constructing local section and the lower bound using isomorphism between the cohomology of complement and the Orlik-Solomon algebra of corresponding arrangement. The results show that the higher topological complexity of the complement of generic arrangements depends only on the number of dimensions of the space and the number of hyperplanes of the arrangement. The calculated results give us one more example to be able to confirm whether the topological complexity of an arrangement of hyperplanes is combinatorial dependent or not.