The Nielsen kernel of an arbitrary Riemann surface

By considering coverings of surfaces by annuli, we extend previous results concerning the Nielsen kernel of topologically finite Riemann surfaces to arbitrary orbifolds. Specifically, we show that the length of a boundary loop in the Nielsen kernel is strictly greater than twice the length of the corresponding boundary loop of its orbifold, and that the infinite Nielsen kernel has empty interior. 2000 Mathematics Subject Classification 30F99 (primary), 30F60 (secondary).