Path-crossing exponents and the external perimeter in 2D percolation

2D percolation path exponents x(l)(P) describe probabilities for traversals of annuli by l nonoverlapping paths on either occupied or vacant clusters, with at least one of each type. We relate the probabilities rigorously to amplitudes of O(N = 1) models whose exponents, believed to be exact, yield x(l)(P) (l(2) - 1)/12. This extends to half-integers the Saleur-Duplantier exponents for k = l/2 clusters, yields the exact fractal dimension of the e xternal cluster perimeter, D-EP = 2 - x(3)(P) = 4/3, and also explains the absence of narrow gate fjords, which was originally noted by Grossman and A harony.