Tight and overtwisted contact structures

2025/04/17 by John B. Etnyre, Etnyre, John B.
Mathematics · Engineering · #Geometric and Algebraic Topology #Control and Stability of Dynamical Systems #Advanced Materials and Mechanics

paper · pdf · doi:10.48550/arxiv.2504.13096

Abstract

The tight versus overtwisted dichotomy has been an essential organizing principle and driving force in 3-dimensional contact geometry since its inception around 1990. In this article, we will discuss the genesis of this dichotomy in Eliashberg's seminal work and his influential contributions to the theory.

Related

• The topology and geometry of contact structures in dimension three
• A proof of the classification theorem of overtwisted contact structures via convex surface theory
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• 3-dimensional methods in contact geometry
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