## 58 Citations

### An adjunction criterion in almost-complex 4-manifolds

- Mathematics
- 2021

The adjunction inequality is a key tool for bounding the genus of smoothly embedded surfaces in 4-manifolds. Using gauge-theoretic invariants, many versions of this inequality have been established…

### Contact 5-manifolds and smooth structures on Stein 4-manifolds

- Mathematics
- 2016

We show that, under a certain condition, contact 5-manifolds can `coarsely' distinguish smooth structures on compact Stein 4-manifolds via contact open books. We also give a simple sufficient…

### Topology of symplectic fillings of contact 3-manifolds

- Mathematics
- 2014

These are some lecture notes for my mini-course in the Gradu ate Workshop on 4-Manifolds, August 18-22, 2014 at the Simons Center for G eometry and Physics. Most of this manuscript is an adaptation…

### Correction to: Stein and Weinstein structures on disk cotangent bundles of surfaces

- MathematicsArchiv der Mathematik
- 2019

In 1998, Gompf described a Stein domain structure on the disk cotangent bundle of any closed surface S, by a Legendrian handlebody diagram. We prove that the boundary of this Stein domain is…

### Relative genus bounds in indefinite four-manifolds

- Mathematics
- 2020

. Given a closed four-manifold X with an indefinite intersection form, we consider smoothly embedded surfaces in X \ ˚ B 4 , with boundary a knot K ⊂ S 3 . We give several methods to bound the genus…

### Symplectic 4–manifolds, Stein domains, Seiberg–Witten theory and mapping class groups

- Mathematics
- 2015

It is less transparent how mapping class groups are related to 4–dimensional topology. By results of Donaldson and Gompf, closed symplectic manifolds (admitting Lefschetz fibration or Lefschetz…

### Exotic ribbon disks and symplectic surfaces.

- Mathematics
- 2020

We construct pairs of surfaces in symplectic 4-manifolds that are topologically isotopic yet are not equivalent under any ambient diffeomorphism, including the first such examples of holomorphic…

### Geodesible contact structures on $3$–manifolds

- Mathematics
- 2008

In this paper, we study and almost completely classify contact structures on closed 3‐ manifolds which are totally geodesic for some Riemannian metric. Due to previously known results, this amounts…

## References

SHOWING 1-10 OF 30 REFERENCES

### A NOTE ON CONTACT STRUCTURES

- Mathematics
- 1998

We construct two contact structures on a homology sphere M , that are homotopic through 2-plane fields, but are not isotopic as contact structures. A diffeomorphism of M permutes these two contact…

### 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…

### 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…

### A product formula for the seiberg-witten invariants and the generalized thom conjecture

- Mathematics
- 1996

The Thorn Conjecture asserts that any compact, embedded surface in CP of degree d > 0 must have genus at least as large as the smooth algebraic curve of the same degree, namely (d — l)(d — 2)/2. More…

### IMMERSED SPHERES IN 4-MANIFOLDS AND THE IMMERSED THOM CONJECTURE

- Mathematics
- 1995

The introduction of the Seiberg Witten monopole equations ([SW1],[SW2],[W]) has served to make the study of smooth 4-manifolds more accessible. Many of the important earlier theorems regarding…

### A fake compact contractible 4-manifold

- Mathematics
- 1991

Here we construct a fake smooth structure on a compact contractible 4-manifold W , where W is a well-known Mazur manifold obtained by attaching in two-handle to S x B along its boundary as in Figure…

### Geometry of Low-dimensional Manifolds: Filling by holomorphic discs and its applications

- Mathematics
- 1991

The survey is devoted to application of the technique of filling by holomorphic discs to different symplectic and complex analytic problems. COMPLEX AND SYMPLECTIC RECOLLECTIONS J -Convexity Let X, J…

### The Genus of Embedded Surfaces in the Projective Plane

- Mathematics
- 1994

1. Statement of the result The genus of a smooth algebraic curve of degree d in CP is given by the formula g = (d − 1)(d − 2)/2. A conjecture sometimes attributed to Thom states that the genus of the…

### Symplectic Geometry: An Introduction based on the Seminar in Bern, 1992

- Mathematics
- 1994

1 Introduction.- 2 Darboux' Theorem and Examples of Symplectic Manifolds.- 3 Generating Functions.- 4 Symplectic Capacities.- 5 Floer Homology.- 6 Pseudoholomorphic Curves.- 7 Gromov's Compactness…

### THE SEIBERG-WITTEN INVARIANTS AND SYMPLECTIC FORMS

- Mathematics
- 1994

(Note: There are no symplectic forms on X unless b and the first Betti number of X have opposite parity.) In a subsequent article with joint authors, a vanishing theorem will be proved for the…