Generalizations of twists of contact structures to higher-dimensions via round surgery

Jiro Adachi

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arXiv · 1610.09672

Generalizations of twists of contact structures to higher-dimensions via round surgery

Jiro Adachi

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Abstract

Twists of contact structures in dimension 3 and higher are studied in this paper from a viewpoint of contact round surgery. Three kinds of new modifications of contact structures which are higher-dimensional generalizations of the $3$-dimensional Lutz twists are introduced. One of the operations makes a contact manifold overtwisted in any dimension. Another one makes it weakly symplectically non-fillable. And the other one makes it strongly symplectically non-fillable. In other words, they make the overtwisted disc, the bordered Legendrian open books, and the Giroux domains, respectively. The first two modifications can be realized by sequences of contact round surgeries. The first operation can be applied anywhere of any contact manifold easily. Further, a version of the first operation keeps the homotopy classes of contact structures as almost contact structures, and the other version contributes to the Euler classes of contact structures.

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Jiro Adachi. 2016-10-30. Generalizations of twists of contact structures to higher-dimensions via round surgery. https://arxiv.org/abs/1610.09672

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