Mapping class group relations, Stein fillings, and planar open book decompositions - Mathematics > Geometric TopologyReport as inadecuate




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Abstract: The aim of this paper is to use mapping class group relations to approach the`geography- problem for Stein fillings of a contact 3-manifold. In particular,we adapt a formula of Endo and Nagami so as to calculate the signature of suchfillings as a sum of the signatures of basic relations in the monodromy of arelated open book decomposition. We combine this with a theorem of Wendl toshow that for any Stein filling of a contact structure supported by a planaropen book decomposition, the sum of the signature and Euler characteristicdepends only on the contact manifold. This gives a simple obstruction toplanarity, which we interpret in terms of existence of certain configurationsof curves in a factorization of the monodromy. We use these techniques todemonstrate examples of non-planar structures which cannot be shown non-planarby previously existing methods.



Author: Andy Wand

Source: https://arxiv.org/



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