Abstract
The characteristic foliation of a sphere embedded in the standard tight contact structure (R3, ζ0) is unique up to isotopy. We show that any Morse-Smale foliation on the sphere with null Euler class, is, up to isotopy, the characteristic foliation of a sphere embedded in the standard overtwisted contact structure (R3, ζ1). We thus have a new way of looking at the two standard structures as ‘opposites’ in the world of contact structures.
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Giorgi, E.E. Characteristic Foliations of Spheres Embedded in the Standard Overtwisted Structure (R3, ζ1). Geometriae Dedicata 78, 49–62 (1999). https://doi.org/10.1023/A:1005003431066
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DOI: https://doi.org/10.1023/A:1005003431066