Tight Contact Structures on Lens Spaces

@article{Etnyre1998TightCS,
  title={Tight Contact Structures on Lens Spaces},
  author={John B. Etnyre},
  journal={Communications in Contemporary Mathematics},
  year={1998},
  volume={02},
  pages={559-577}
}
  • J. Etnyre
  • Published 10 December 1998
  • Mathematics
  • Communications in Contemporary Mathematics
In this paper we develop a method for studying tight contact structures on lens spaces. We then derive uniqueness and non-existence statements for tight contact structures with certain (half) Euler classes on lens spaces. 

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References

SHOWING 1-10 OF 32 REFERENCES

On the classification of tight contact structures I

We develop new techniques in the theory of convex surfaces to prove complete classication results for tight contact structures on lens spaces, solid tori, and T 2 I .

TOPOLOGICAL CHARACTERIZATION OF STEIN MANIFOLDS OF DIMENSION >2

In this paper I give a completed topological characterization of Stein manifolds of complex dimension >2. Another paper (see [E14]) is devoted to new topogical obstructions for the existence of a

The classification of tight contact structures on the 3-torus

A contact structure £ on a 3-manifold M is called tight if the characteristic foliation of any embedded disc D has no limit cycle, and £ is called overtwisted if otherwise. The classification of over

Tight contact structures via dynamics

We consider the problem of realizing tight contact structures on closed orientable three-manifolds. By applying the theorems of Hofer et al., one may deduce tightness from dynamical properties of

4-manifolds and Kirby calculus

4-manifolds: Introduction Surfaces in 4-manifolds Complex surfaces Kirby calculus: Handelbodies and Kirby diagrams Kirby calculus More examples Applications: Branched covers and resolutions Elliptic

Tight contact structures on solid tori

In this paper we study properties of tight contact structures on solid tori. In particular we discuss ways of distinguishing two solicl tori with tight contact structures. We also give examples of

Tight contact structures and Seiberg–Witten invariants

Contact structures are the odd-dimensional analogue of symplectic structures. Although much is known, the present understanding of both kinds of structures is far from complete, even in low

Contact Topology and Hydrodynamics

We draw connections between the field of contact topology and the study of Beltrami fields in hydrodynamics on Riemannian manifolds in dimension three. We demonstrate an equivalence between Reeb

Handlebody construction of Stein surfaces

The topology of Stein surfaces and contact 3-manifolds is studied by means of handle decompositions. A simple characterization of homeomorphism types of Stein surfaces is obtained-they correspond to