Related papers: Symplectic surgeries and normal surface singularit…

Suppose that $C=(C_1,..., C_m)$ is a configuration of 2-dimensional symplectic submanifolds in a symplectic 4-manifold $(X,\omega)$ with connected, negative definite intersection graph $\Gamma_C$. We show that by replacing an appropriate…

We prove that if a symplectic 4-manifold $X$ becomes a rational 4-manifold after applying rational blow-down surgery, then the symplectic 4-manifold $X$ is originally rational. That is, a symplectic rational blow-up of a rational symplectic…

We study neighborhoods of configurations of symplectic surfaces in symplectic 4-manifolds. We show that suitably `positive' configurations have neighborhoods with concave boundaries and we explicitly describe open book decompositions of the…

We prove that the generalized rational blowdown, a surgery on smooth 4-manifolds, can be performed in the symplectic category.

We investigate the notion of symplectic divisorial compactification for symplectic 4-manifolds with either convex or concave type boundary. This is motivated by the notion of compactifying divisors for open algebraic surfaces. We give a…

We prove that the rational blowdown, a surgery on smooth 4-manifolds introduced by Fintushel and Stern, can be performed in the symplectic category. As a consequence, interesting families of smooth 4-manifolds, including the exotic $K3$…

We construct simply connected, minimal, symplectic 4-manifolds with exotic smooth structures and each with one Seiberg-Witten basic class up to sign, on the Noether line and between the Noether and half Noether lines by star surgeries…

Fintushel and Stern defined the rational blow-down construction [FS] for smooth 4-manifolds, where a linear plumbing configuration of spheres $C_n$ is replaced with a rational homology ball $B_n$, $n \geq 2$. Subsequently, Symington [Sy]…

We describe a variety of symplectic surgeries (not a priori compatible with Kahler structures) which are obtained by combining local Kahler degenerations and resolutions of singularities. The effect of the surgeries is to replace…

We give finiteness results and some classifications up to diffeomorphism of minimal strong symplectic fillings of Seifert fibered spaces over S^2 satisfying certain conditions, with a fixed natural contact structure. In some cases we can…

We define a new 4-dimensional symplectic cut and paste operation which is analogous to Fintushel and Stern's rational blow-down. We use this operation to produce multiple constructions of symplectic smoothly exotic complex projective space…

In this article we construct a new family of simply connected symplectic 4-manifolds with $b_2^+ =1$ and $c_1^2 =2$ which are not diffeomorphic to rational surfaces by using rational blow-down technique. As a corollary, we conclude that a…

We show that there is a complex structure on the symplectic 4-manifold $W_{4, k}$ obtained from the elliptic surface E(4) by rationally blowing down $k$ sections for $2\le k\le 9$. And we interpret it via ${\mathbb Q}$-Gorenstein smoothing.…

We give two constructions of surfaces in simply-connected 4-manifolds with non simply-connected complements. One is an iteration of the twisted rim surgery introduced by the first author. We also construct, for any group G satisfying some…

We introduce a method to resolve a symplectic orbifold into a smooth symplectic manifold. Then we study how the formality and the Lefschetz property of the symplectic resolution are compared with that of the symplectic orbifold. We also…

We show that a minimal surface of general type has a canonical symplectic structure (unique up to symplectomorphism) which is invariant for smooth deformation. We show that the symplectomorphism type is also invariant for deformations which…

Previously work of the author with Meier and Starkston showed that every closed symplectic manifold $(X,\omega)$ with a rational symplectic form admits a trisection compatible with the symplectic topology. In this paper, we describe the…

We show that under appropriate hypotheses, a plumbing of symplectic surfaces in a symplectic 4-manifold admits strongly convex neighborhoods. Moreover the neighborhoods are Lefschetz fibered with an easily-described open book on the…

In this paper we give a necessary combinatorial condition for a negative--definite plumbing tree to be suitable for rational blow--down, or to be the graph of a complex surface singularity which admits a rational homology disk smoothing.…

We establish various stability results for symplectic surfaces in symplectic $4-$manifolds with $b^+=1$. These results are then applied to prove the existence of representatives of Lagrangian ADE-configurations as well as to classify…