Related papers: Exotic rational elliptic surfaces without 1-handle…

We formulate a very general conjecture relating the analytical invariants of a normal surface singularity to the Seiberg-Witten invariants of its link provided that the link is a rational homology sphere. As supporting evidence, we…

By extending a result of Kronheimer-Mrowka to the family setting, we prove a gluing formula for the family Seiberg-Witten invariant. This formula allows one to compute the invariant for a smooth family of 4-manifolds by cutting it open…

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 of a non-K\"{a}hler complex surface, which…

We construct an invariant of closed ${\rm spin}^c$ 4-manifolds using families of Seiberg-Witten equations. This invariant is formulated as a cohomology class on a certain abstract simplicial complex consisting of embedded surfaces of a…

In this paper we show that the Seiberg--Witten invariant is zero for all smooth 4--manifolds with $b_+{>}1$ which admit circle actions that have at least one fixed point. Furthermore, we show that all symplectic 4--manifolds which admit…

From a handlebody-theoretic perspective, the simplest compact, contractible 4-manifolds, other than the 4-ball, are Mazur manifolds. We produce the first pairs of Mazur manifolds that are homeomorphic but not diffeomorphic. Our…

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…

We construct four-dimensional symplectic cobordisms between contact three-manifolds generalizing an example of Eliashberg. One key feature is that any handlebody decomposition of one of these cobordisms must involve three-handles. The other…

Motivated by a recent result of Y. Lee and the second author[7], we construct a simply connected minimal complex surface of general type with p_g=0 and K^2=3 using a rational blow-down surgery and Q-Gorenstein smoothing theory. In a similar…

Round handles are affiliated with smooth 4-manifolds in two major ways: 5-dimensional round handles appear extensively as the building blocks in cobordisms between 4-manifolds, whereas 4-dimensional round handles are the building blocks of…

Symplectic 4-manifolds $(X,\omega)$ with $b_+{=}1$ are roughly classified by the canonical class $K$ and the symplectic form $\omega$ depending upon the sign of $K^2$ and $K\cdot \omega$. Examples are known for each category except for the…

We study smooth, proper embeddings of noncompact surfaces in 4-manifolds, focusing on exotic planes and annuli, i.e., embeddings pairwise homeomorphic to the standard embeddings of R^2 and R^2-int D^2 in R^4. We encounter two uncountable…

We construct a (smooth, projective) surface over the field of rational numbers, which is a counterexample to the Hasse principle not accounted for by the Manin obstruction. The construction relies on the classical 4-descent on elliptic…

We calculate the Seiberg-Witten invariants of branched covers of prime degree, where the branch locus consists of embedded spheres. Aside from the formula itself, our calculations give rise to some new constraints on configurations of…

We show the existence of hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants, addressing a conjecture of Claude LeBrun. This is achieved by showing, using results in geometric and arithmetic group theory, that certain hyperbolic…

From any 4-dimensional oriented handlebody X without 3- and 4-handles and with b_2>0, we construct arbitrary many compact Stein 4-manifolds which are mutually homeomorphic but not diffeomorphic to each other, so that their topological…

We verify that the rational blow-down schemes along certain Seifert fibered 3-manifolds found by the second author, Szabo and Wahl are, in fact, symplectic operations.

We construct closed, aspherical, smooth 4-manifolds that are homeomorphic but not diffeomorphic. These provide counterexamples to a smooth analog of the Borel conjecture in dimension four. Our technique is to apply the `reflection group…

Using orbifold Hilbert schemes, we compactify all two-dimensional Hitchin systems corresponding to types A0-tilde, D4-tilde, E6-tilde, E7-tilde, and E8-tilde, thereby obtaining four rational elliptic surfaces with C*-actions. Their singular…

We prove that every 4-dimensional oriented handlebody without 3- and 4-handles can be modified to admit infinitely many exotic smooth structures, and moreover prove that their genus functions are pairwise equivalent. We furthermore show…