Related papers: The simple type conjecture for mod 2 Seiberg-Witte…
The goal of this paper is to demonstrate that, at least for nonsimply connected 4-manifolds, the Seiberg-Witten invariant alone does not determine diffeomorphism type within the same homeomorphism type.
A formula is given for the Seiberg-Witten invariants of a 4-manifold that is cut along certain kinds of 3-dimensional tori. The formula involves a Seiberg-Witten invariant for each of the resulting pieces.
We use rudiments of the Seiberg-Witten gluing theory for trivial circle bundles over a Riemann surface to relate de Seiberg-Witten basic classes of two $4$-manifolds containing Riemann surfaces of the same genus and self-intersection zero…
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…
Closed oriented 4-manifolds with the same geometrically 2-dimensional fundamental group (satisfying certain properties) are classified up to $s$-cobordism by their $w_2$-type, equivariant intersection form and the Kirby-Siebenmann…
In this paper, we demonstrate a relation among Seiberg-Witten invariants which arises from embedded surfaces in four-manifolds whose self-intersection number is negative. These relations, together with Taubes' basic theorems on the…
By extending the notion of simple type for the Seiberg--Witten invariant of a 4-manifold, we introduce notions of BF blowup simple type and BF homogeneous type for the Bauer--Furuta invariant and study their applications. Specifically, we…
This article presents the constructions of new infinite families of smooth 4-manifolds with the property that any two manifolds in the same family are homeomorphic and, from their construction, seem to be quite different, but cannot be…
It is shown that there are infinitely many compact orientable smooth 4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality 2 chi > 3 |tau|. The examples in question arise as…
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…
For each nonnegative integer m we show that any closed, oriented topological four-manifold with fundamental group Z_{4m+2} and odd intersection form, with possibly seven exceptions, either admits no smooth structure or admits infinitely…
We show examples of pairs of smooth, compact, homeomorphic 4-manifolds, whose diffeomorphism types are distinguished by the topology of the singular sets of smooth stable maps defined on them. In this distinction we rely on results from…
We shall prove a new non-vanishing theorem for the stable cohomotopy Seiberg-Witten invariant of connected sums of 4-manifolds with positive first Betti number. The non-vanishing theorem enables us to find many new examples of 4-manifolds…
This is the sequel to the author's previous paper which gives an extension of Taubes' "SW=Gr" theorem to non-symplectic 4-manifolds. The main result of this paper asserts the following. Whenever the Seiberg-Witten invariants are defined…
This article presents a new and more elementary proof of the main Seiberg-Witten-based obstruction to the existence of Einstein metrics on smooth compact 4-manifolds. It also introduces a new smooth manifold invariant which conveniently…
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…
We show that every smooth closed oriented four-manifold admits a decomposition into two co- dimension zero submanifolds with common boundary. Each of these submanifolds carries a structure of a symplectic manifold with pseudo-convex…
On a smooth closed oriented $4$-manifold $M$ with a smooth action of a finite group $G$ on a Spin$^c$ structure, $G$-monopole invariant is defined by "counting" $G$-invariant solutions of Seiberg-Witten equations for any $G$-invariant…
The main result of this paper is a formula for calculating the Seiberg-Witten invariants of 4-manifolds with fixed-point free circle actions. This is done by showing under suitable conditions the existence of a diffeomorphism between the…
On a compact oriented four-manifold with an orientation preserving involution c, we count solutions of Seiberg-Witten equations, which are moreover symmetrical in relation to c, to construct "real" Seiberg-Witten invariants. Using Taubes'…