Minimal atlases of closed contact manifolds
Abstract
We study the minimal number C(M,) of contact charts that one needs to cover a closed connected contact manifold (M,). Our basic result is C(M,) M + 1. We compute C(M,) for all closed connected contact 3-manifolds: C (M,) = 2 if M = S3 and is tight, 3 if M = S3 and is overtwisted or if M = #k (S2 × S1), 4 otherwise. We also show that on every sphere S2n+1 there exists a contact structure with C(S2n+1,) 3.
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