THE HIGHER TOPOLOGICAL COMPLEXITY OF A COMPLEMENT OF COMPLEX LINES ARRANGEMENT

Abstract

The Riemann compact surface Sigmag is an oriented two-dimensional compact manifold. This geometry object in R 3 has many beautiful geometrical properties and is interested in much research in differential geometry. Higher topological complexity is a topological invariant introduced by Y. B. Rudyak in 2010, which is a general concept of topological complexcity. Related problems of topological complexity and higher topological complexit have been mentioned in a lot of studies to solve some problems in robotic theory in recent years. In this paper, we give the results of calculating the high order topological complexity of the oriented Riemann compact surface with genus g.