Open book decompositions of links of quotient surface singularities and support genus problem

Details Open book decompositions of links of quotient surface singularities and support genus problem Open book decompositions of links of quotient surface singularities and support genus problem

2012-04-16

arxiv.org/abs/1204.3576v1

Mathematics

Geometric Topology

26 pages, 20 figures

Scientific paper

In this paper we write explicitly the open book decompositions of links of quotient surface singularities supporting the corresponding unique Milnor fillable contact structure. The page-genus of these Milnor open books are minimal among all Milnor open books supporting the same contact structure. We also investigate whether the Milnor genus is equal to the support genus for links of quotient surface singularities. We show that for many types of the quotient surface singularities the Milnor genus is equal to the support genus. In the remaining cases we are able to find a small upper bound for the support genus.

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