Geometric criteria for overtwistedness
classification
🧮 math.SG
keywords
overtwistedcriteriageometricmanifoldovertwistednessapplicationsbookcharacterize
read the original abstract
We establish geometric criteria to decide whether a contact manifold is overtwisted. Starting with the original definition, we first relate the different overtwisted disks in each dimension and show that a manifold is overtwisted if the Legendrian unknot is loose. Then we characterize overtwistedness in terms of open book decompositions and provide several applications.
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