Planar Contact Structures with Binding Number Three

Details Planar Contact Structures with Binding Number Three Planar Contact Structures with Binding Number Three

2007-11-12

arxiv.org/abs/0711.1774v2

Mathematics

Geometric Topology

35 pages, 19 figures, 9 tables (published version)

Scientific paper

In this article, we find the complete list of all contact structures (up to isotopy) on closed three-manifolds which are supported by an open book decomposition having planar pages with three (but not less) boundary components. We distinguish them by computing their first Chern classes and three dimensional invariants (whenever possible). Among these contact structures we also distinguish tight ones from those which are overtwisted.

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