THE HIGHER TOPOLOGICAL COMPLEXITY OF BRAID ARRANGEMENTS

Abstract

The concept of topological complexity of topological space was introduced by M.Faber in 2001. In 2010, by generalizing this concept, Y.B. Rudyak introduced the concept of higher topological complexity. In this paper, we calculate the higher topological complexity for the complement of Braid arrangements in complex vector space. To do this, we estimate the upper bound by construct a series of projections, provide the relationship between the overall space with the projection space and the grain of the projections and give the lower bound by using the property of genered element of Orlik-Solomon algebra. By application this results, we give the result about the higher topological complexity of configuration space on real plane.