Minimal atlases of closed contact manifolds
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We study the minimal number C(M,ξ) of contact charts that one needs to cover a closed connected contact manifold (M,ξ). Our basic result is C(M,ξ) \le \dim M + 1.
We compute C(M,ξ) for all closed connected contact 3-manifolds:
C (M,ξ) = 2 if M = S^3 and ξis tight,
3 if M = S^3 and ξis 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},ξ) \ge 3.
40 pages, 18 figures
40 pages, 18 figures