A topological view of the Nevanlinna-Pick problem: Solutions of dimension n

Based on a topological property of a certain map we establish that when the (n+1)-point Nevanlinna-Pick problem is solvable, then for any dissipation polynomial of degree n or less, there corresponds an interpolating function with dimension at most n. Our results provide a topological proof for the sufficiency of Pick´s criterion for the solvability of the Nevanlinna-Pick problem.