Minimal atlases of closed contact manifolds

Details Minimal atlases of closed contact manifolds Minimal atlases of closed contact manifolds

2008-07-18

arxiv.org/abs/0807.3047v1

Mathematics

Symplectic Geometry

40 pages, 18 figures

Scientific paper

We study the minimal number C(M,\xi) of contact charts that one needs to cover a closed connected contact manifold (M,\xi). Our basic result is C(M,\xi) \le \dim M + 1. We compute C(M,\xi) for all closed connected contact 3-manifolds: C (M,\xi) = 2 if M = S^3 and \xi is tight, 3 if M = S^3 and \xi is overtwisted or if M = #_k (S^2 \times S^1), 4 otherwise. We also show that on every sphere S^{2n+1} there exists a contact structure with C(S^{2n+1},\xi) \ge 3.

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