Open books decompositions of links of minimally elliptic singularities

Abstract

We present an explicit Milnor open book decomposition supporting the canonical contact structure on the link of each minimally elliptic singularity whose fundamental cycle satisfies −3 ≤ ⋅ ≤ −1. For the Milnor open books whose pages have genus less than three, we give a factorization of the monodromy which does not involve any left-handed Dehn twists around interior curves. Necessary results regarding the roots of reducible, and irreducible elements in mapping class groups are proved, and some new relations in the mapping class groups are presented.