In this article we classify up to isotopy the tight contact structures on Seifert manifolds over the torus with one singular fibre.

Contact homology for Legendrian submanifolds in standard contact (2n + 1)space is rigorously defined using moduli spaces of holomorphic disks with Lagrangian boundary conditions in complex n-space. The homology provides new invariants of Legendrian isotopy. These invariants show that the theory of Legendrian isotopy is very rich. For example, they detect infinite families of pairwise non-isotop...

A theorem of William Jaco and Eric Sedgwick states that if M is an irreducible, ∂-irreducible 3-manifold with boundary a single torus, and if M contains no genus one essential (incompressible and ∂-incompressible) surfaces, then M cannot contain infinitely many distinct isotopy classes of essential surfaces of uniformly bounded genus. The main result in this paper is a generalization: If M is a...

Together with M. Boyle and D. Huang (2000), this paper gives an alternate development of the Huang classification of shifts of finite type up to flow equivalence, and provides additional functorial information, used to analyze the action of the mapping class group of the mapping torus of a shift of finite type on the “isotopy futures” group, which is introduced here. For a shift of finite type ...

Any 2-bridge knot in S has a bridge sphere from which any other bridge surface can be obtained by stabilization, meridional stabilization, perturbation and proper isotopy.