Classification of oriented Montesinos links by invariants of spin structures

In this paper we give the isotopy classification of oriented Montesinos links. The definition of the invariants of links needed for this and the proof of the classification theorem are based on a new construction, which establishes a correspondence between orientations of a link $l\subset S^n$ on the one hand, and spin structures on the two-sheeted branched covering of the sphere, branched over $l$, on the other. New numerical invariants of spin structures on three-dimensional Seifert manifolds are introduced in the paper; these invariants are used to classify the Montesinos links.