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Gluing tight contact structures

Ko Honda
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Abstract

We prove gluing theorems for tight contact structures. In particular, we rederive (as special cases) gluing theorems due to Colin and Makar-Limanov, and present an algorithm for determining whether a given contact structure on a handlebody is tight. As applications, we construct a tight contact structure on a genus 4 handlebody which becomes overtwisted after Legendrian -1 surgery, and study certain Legendrian surgeries on T^3.

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Ko Honda. 2001-02-04. Gluing tight contact structures. https://arxiv.org/abs/math/0102029

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