A Note on Overtwisted Contact Structures
Elif Yilmaz
TL;DR
This paper demonstrates that certain closed contact 3-manifolds with open book decompositions having monodromies as products of left-handed Dehn twists are overtwisted, utilizing recent Honda-Kazez-Matic results.
Contribution
It establishes a new criterion for overtwistedness in contact 3-manifolds based on open book monodromy composition.
Findings
Contact 3-manifolds with specific open book monodromies are overtwisted
Utilizes recent Honda-Kazez-Matic work to prove overtwistedness
Provides a new perspective on contact structure classification
Abstract
In this note, we use the recent work of Honda-Kazez-Matic [HKM] to prove that a closed contact 3-manifold admitting a compatible open book decomposition with a nontrivial monodromy which can be presented as a product of left handed Dehn twists is overtwisted.
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Taxonomy
TopicsStructural Analysis and Optimization · Structural Analysis of Composite Materials