Tight and overtwisted contact structures

2025/04/17 by John B. Etnyre, Etnyre, John B. · 1 voice
Engineering · Mathematics · #Advanced Materials and Mechanics #Control and Stability of Dynamical Systems #Geometric and Algebraic Topology #math.GT #math.SG

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.

Citations

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Discussions

• John B. Etnyre: Tight and overtwisted contact structures https://arxiv.org/abs/2504.13096 https://arxiv.org/pdf/2504.13096 https://arxiv.org/html/2504.13096 [bsky, 0 points, 1 comments]

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
• Bypass attachments in higher-dimensional contact topology
• 3-dimensional methods in contact geometry
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