Wand, A. (2012) Mapping class group relations, Stein fillings, and planar open book decompositions. Journal of Topology, 5(1), pp. 1-14. (doi: 10.1112/jtopol/jtr025)
Full text not currently available from Enlighten.
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 such fillings as a sum of the signatures of basic relations in the monodromy of a related open book decomposition. We combine this with a theorem of Wendl to show that, for any Stein filling of a contact structure supported by a planar open book decomposition, the sum of the signature and Euler characteristic depends only on the contact manifold. This gives a simple obstruction to planarity, which we interpret in terms of the existence of certain configurations of curves in a factorization of the monodromy. We use these techniques to demonstrate examples of non-planar structures that cannot be shown to be non-planar by other existing methods.
Item Type: | Articles |
---|---|
Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Wand, Dr Andy |
Authors: | Wand, A. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Journal of Topology |
Publisher: | Oxford University Press |
ISSN: | 1753-8416 |
ISSN (Online): | 1753-8424 |
University Staff: Request a correction | Enlighten Editors: Update this record