# Orbifold adjunction formula and symplectic cobordisms between lens spaces

@article{Chen2004OrbifoldAF, title={Orbifold adjunction formula and symplectic cobordisms between lens spaces}, author={Weimin Chen}, journal={Geometry \& Topology}, year={2004}, volume={8}, pages={701-734} }

Each lens space has a canonical contact structure which lifts to the distribution of complex lines on the three-sphere. In this paper, we show that a symplectic homology cobordism between two lens spaces, which is given with the canonical contact structure on the boundary, must be dieomorphic to the product of a lens space with the unit interval. As one of the main ingredients in the proof, we also derive in this paper the adjunction and intersection formulae for pseudoholomorphic curves in an… Expand

#### 20 Citations

Smooth s-cobordisms of elliptic 3-manifolds

- Mathematics
- 2004

The main result of this paper states that a symplectic s-cobordism of elliptic 3-manifolds is diffeomorphic to a product (assuming a canonical contact structure on the boundary). Based on this… Expand

On a notion of maps between orbifolds I. Function spaces

- Mathematics
- 2006

This is the first of a series of papers which is devoted to a comprehensive theory of maps between orbifolds. In this paper, we define the maps in the more general context of orbispaces, and… Expand

Pseudoholomorphic curves in four-orbifolds and some applications

- Mathematics
- 2004

The main purpose of this paper is to summarize the basic ingredients, illustrated with examples, of a pseudoholomorphic curve theory for symplectic 4-orbifolds. These are extensions of relevant work… Expand

ON A NOTION OF MAPS BETWEEN ORBIFOLDS II: HOMOTOPY AND CW-COMPLEX

- Mathematics
- 2006

This is the second of a series of papers which is devoted to a comprehensive theory of maps between orbifolds. In this paper, we develop a basic machinery for studying homotopy classes of such maps.… Expand

Holomorphic curves in the symplectizations of lens spaces: an elementary approach

- Mathematics
- 2020

We present an elementary computational scheme for the moduli spaces of rational pseudo-holomorphic curves in the symplectizations of 3-dimensional lens spaces, which are equipped with Morse-Bott… Expand

Seiberg-Witten invariants of 3-orbifolds and non-Kähler surfaces

- Mathematics
- 2011

A formula is given which computes the Seiberg-Witten invariant of a 3-orbifold from the invariant of the underlying manifold. As an application, we derive a formula for the Seiberg-Witten invariant… Expand

Seifert fibered four-manifolds with nonzero Seiberg-Witten invariant

- Mathematics
- 2011

The main result of this paper asserts that if a Seifert fibered 4-manifold has nonzero Seiberg-Witten invariant, the homotopy class of regular fibers has infinite order. This is a nontrivial… Expand

Resolving symplectic orbifolds with applications to finite group actions

- Mathematics
- 2017

We associate to each symplectic 4-orbifold X a canonical smooth symplectic resolution π : X̃ → X, which can be done equivariantly if X comes with a symplectic G-action by a finite group. Moreover, we… Expand

On almost complex embeddings of rational homology balls

- Mathematics
- 2020

We use elementary arguments to prove that none of the Stein rational homology 4-balls shown by the authors and Brendan Owens to embed smoothly but not symplectically in the complex projective plane… Expand

Infinitely many exotic monotone Lagrangian tori in ℂℙ2

- Mathematics
- 2016

In [10], we construct an exotic monotone Lagrangian torus in CP 2 (not Hamiltonian isotopic to the known Clifford and Chekanov tori) using techniques motivated by mirror symmetry. We named it… Expand

#### References

SHOWING 1-10 OF 34 REFERENCES

On symplectic fillings of lens spaces

- Mathematics
- 2003

Le ξ st be the contact structure naturally induced on the lens space L(p, q) = S 3 /Z/pZ by the standard contact structure ξ st on the three-sphere S 3 . We obtain a complete classification of the… Expand

On a notion of maps between orbifolds I. Function spaces

- Mathematics
- 2006

This is the first of a series of papers which is devoted to a comprehensive theory of maps between orbifolds. In this paper, we define the maps in the more general context of orbispaces, and… Expand

Gromov’s Compactness Theorem for Pseudo-holomorphic Curves

- Mathematics
- 2004

Mikhail Gromov introduced pseudo-holomorphic curves into symplectic geometry in 1985. This book aims to present in detail the original proof for Gromov's compactness theorum for pseudo-holomorphic… Expand

J-Holomorphic Curves and Symplectic Topology

- Mathematics
- 2004

The theory of $J$-holomorphic curves has been of great importance since its introduction by Gromov in 1985. In mathematics, its applications include many key results in symplectic topology. It was… Expand

Singularities and positivity of intersections of J-holomorphic curves

- Mathematics
- 1994

This chapter is devoted to proving some of the main technical results about J-holomorphic curves which make them such a powerful tool when studying the geometry of symplectic 4-manifolds. We begin by… Expand

The local behaviour of holomorphic curves in almost complex 4-manifolds

- Mathematics
- 1991

In this paper we prove various results about the positivity of intersections of holomorphic curves in almost complex 4-manifolds which were stated by Gromov. We also show that the virtual genus of… Expand

Pseudo holomorphic curves in symplectic manifolds

- Mathematics
- 1985

Definitions. A parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J). The image C=f(S)C V is called… Expand

Pseudo-holomorphic maps and bubble trees

- Mathematics
- 1993

This paper proves a strong convergence theorem for sequences of pseudo-holomorphic maps from a Riemann surface to a symplectic manifoldN with tamed almost complex structure. (These are the objects… Expand

Holomorphic curves in symplectic geometry

- Mathematics
- 1994

Introduction: Applications of pseudo-holomorphic curves to symplectic topology.- 1 Examples of problems and results in symplectic topology.- 2 Pseudo-holomorphic curves in almost complex manifolds.-… Expand

On Positive Sasakian Geometry

- Mathematics
- 2001

AbstractA Sasakian structure
$$\mathcal{S}$$
=(\xi,\eta,\Phi,g) on a manifold Mis called positiveif its basic first Chern class c1(
$$\mathcal{F}$$
ξ) can be represented by a positive (1,1)-form… Expand