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

Elif Dalyan; Elif Dalyan

doi:10.3934/math.2020005

AIMS Mathematics

2020, Volume 5, Issue 1: 54-78. doi: 10.3934/math.2020005

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Research article

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

Elif Dalyan ^,

Department of Mathematics, Hitit University, Corum, TURKEY

Received: 11 July 2019 Accepted: 24 September 2019 Published: 17 October 2019
MSC : 57R17, 32S55, 32S25

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.
- quotient surface singularities,
- open book decomposition,
- contact structure,
- Milnor genus,
- support genus
Citation: Elif Dalyan. Open book decompositions of links of quotient surface singularities and support genus problem[J]. AIMS Mathematics, 2020, 5(1): 54-78. doi: 10.3934/math.2020005

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Abstract

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.

References

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