A quantum analogue of generic bases for affine cluster algebras

We construct quantized versions of generic bases in quantum cluster algebras of finite and affine types. Under the specialization of $q$ and coefficients to 1, these bases are generic bases of finite and affine cluster algebras.Comment: The paper supersedes arXiv:1006.392

E8E_8-plumbings and exotic contact structures on spheres

We prove the existence of exotic but homotopically trivial contact structures on spheres of dimension 8k-1. Together with previous results of Eliashberg and the second author this establishes the existence of such structures on all odd-dimensional spheres (of dimension at least 3).Comment: 12 page

Contact structures on principal circle bundles

We describe a necessary and sufficient condition for a principal circle bundle over an even-dimensional manifold to carry an invariant contact structure. As a corollary it is shown that all circle bundles over a given base manifold carry an invariant contact structure, only provided the trivial bundle does. In particular, all circle bundles over 4-manifolds admit invariant contact structures. We also discuss the Bourgeois construction of contact structures on odd-dimensional tori in this context, and we relate our results to recent work of Massot, Niederkrueger and Wendl on weak symplectic fillings in higher dimensions.Comment: 14 pages, 1 figure; v2: changes to exposition, Sections 5.2, 5.3 and 6 are ne

A Legendrian surgery presentation of contact 3-manifolds

We prove that every closed, connected contact 3-manifold can be obtained from the 3-sphere with its standard contact structure by contact surgery of coefficient plus or minus 1 along a Legendrian link. As a corollary, we derive a result of Etnyre and Honda about symplectic cobordisms (in slightly stronger form).Comment: 18 pages, Section 3 and three figures added. To appear in Math. Proc. Cambridge Philos. So