# 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} }

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.

## 44 Citations

### On the classification of tight contact structures I

- Mathematics
- 1999

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 .

### On the coarse classification of tight contact structures

- Mathematics
- 2003

We present a sketch of the proof of the following theorems: (1) Every 3-manifold has only finitely many homotopy classes of 2-plane fields which carry tight contact structures. (2) Every closed…

### Tight contact structures on 3-manifolds via dynamics

- Mathematics
- 1998

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…

### On the classification of tight contact structures

- Mathematics
- 2002

Recently, there have been several breakthroughs in the classification of tight contact structures. We give an outline on how to exploit methods developed by Ko Honda and John Etnyre to obtain…

### Tight contact structures with no symplectic fillings

- Physics
- 2000

Abstract.We exhibit tight contact structures on 3-manifolds that do not admit any symplectic fillings.

### Low Dimensional Contact Geometry

- Mathematics

structures. Extending the work of myself and others I shall develop a general framework for understanding Legendrian and transversal knots: for example understand how they behave under connected sums…

### Classification of tight contact structures on a solid torus

- Mathematics, Computer Science
- 2020

This paper answers the classification question completely for the case of a solid torus by writing down a closed formula for the number of non-isotopic tight contact structures with any given dividing set on the boundary of theSolid torus.

### Notes on the isotopy finiteness

- Mathematics
- 2003

This is the less official, English version of the proof of the fact that every closed atoroidal 3-manifold carries finitely many isotopy classes of tight contact structures.

## References

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### On the classification of tight contact structures I

- Mathematics
- 1999

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

- Mathematics
- 1990

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

- Mathematics
- 1997

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

- Mathematics
- 1999

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

- Mathematics
- 1999

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

- Mathematics
- 1998

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

- Mathematics
- 1997

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

- Mathematics
- 1997

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

- Mathematics
- 1998

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…