The Double Cover of S3 Branched along a Link

Abstract

Let L be an unsplittable link in S3 and let V denote the double cover of S3 branched along L. Starting with an arbitrary planar projection of L, it is shown how to construct a special presentation for the fundamental group π1V which encodes in a simple way geometric data from a (checkerboard) spanning surface obtained from the given projection, and which relates to the construction of Coxeter quotients of π1 (S3-L) previously studied by the author and Y. W. Lee.