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A proof of the classification theorem of overtwisted contact structures via convex surface theory. (English) Zbl 1396.57041

Summary: In [Invent. Math. 98, No. 3, 623–637 (1989; Zbl 0684.57012)], Y. Eliashberg proved that two overtwisted contact structures on a closed oriented 3-manifold are isotopic through contact structures if and only if they are homotopic as 2-plane fields. We provide an alternative proof of this theorem using the convex surface theory and bypasses.

MSC:

57R17 Symplectic and contact topology in high or arbitrary dimension
53D35 Global theory of symplectic and contact manifolds
53D10 Contact manifolds (general theory)

Citations:

Zbl 0684.57012
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