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arXiv · 1803.07997

Contactomorphism groups and Legendrian flexibility

Sylvain Courte·Patrick Massot
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Abstract

We explain a connection between the algebraic and geometric properties of groups of contact transformations, open book decompositions, and flexible Legendrian embeddings. The main result is that, if a closed contact manifold $(V, \xi)$ has a supporting open book whose pages are flexible Weinstein manifolds, then the connected component $G$ of the identity in its automorphism group is a uniformly simple group: for every non-trivial element $g$, every other element is a product of at most $128(\dim V + 1)$ conjugates of $g^{\pm 1}$. In particular any conjugation invariant norm on this group is bounded. We also prove the later statement still holds for the universal cover of $G$.

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Sylvain Courte, Patrick Massot. 2018-03-21. Contactomorphism groups and Legendrian flexibility. https://arxiv.org/abs/1803.07997

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