Tight contact structures on some bounded Seifert manifolds with minimal convex boundary

Details Tight contact structures on some bounded Seifert manifolds with minimal convex boundary Tight contact structures on some bounded Seifert manifolds with minimal convex boundary

2011-11-08

arxiv.org/abs/1111.1900v2

Mathematics

Geometric Topology

17 pages, 5 figures

Scientific paper

We classify positive tight contact structures, up to isotopy fixing the boundary, on the manifolds $N=M(D^{2}; r_1, r_2)$ with minimal convex boundary of slope $s$ and Giroux torsion 0 along $\partial N$, where $r_1,r_2\in (0,1)\cap\mathbb{Q}$, in the following cases: (1) $s\in(-\infty, 0)\cup[2, +\infty)$; (2) $s\in[0, 1)$ and $r_1,r_2\in [1/2,1)$; (3) $s\in[1, 2)$ and $r_1,r_2\in(0,1/2)$; (4) $s=\infty$ and $r_1=r_2=1/2$. We also classify positive tight contact structures, up to isotopy fixing the boundary, on $M(D^2;1/2,1/2)$ with minimal convex boundary of arbitrary slope and Giroux torsion greater than 0 along the boundary.

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