Related papers: Seiberg-Witten invariants, orbifolds, and circle a…
In this thesis we study the Seiberg-Witten theory of an oriented homology 3-sphere. The goal is to extract topological invariants - the Seiberg-Witten invariants - by counting the solutions to the Seiberg-Witten equations on the manifold.…
A smooth, compact 4-manifold with a Riemannian metric and b^(2+) > 0 has a non-trivial, closed, self-dual 2-form. If the metric is generic, then the zero set of this form is a disjoint union of circles. On the complement of this zero set,…
We introduce an invariant of tuples of commutative diffeomorphisms on a 4-manifold using families of Seiberg-Witten equations. This is a generalization of Ruberman's invariant of diffeomorphisms defined using 1-parameter families of…
In this paper we describe the Seiberg-Witten invariants, which have been introduced by Witten, for manifolds with $b_+=1$. In this case the invariants depend on a chamber structure, and there exists a universal wall crossing formula. For…
We compute the equivariant Bauer-Furuta degree, when a finite group acts freely on a spin 4-manifold. In the case when the group is cyclic of order power of two, Bryan gave a formula and its applications. We have treated the case when the…
We study relative Seiberg-Witten moduli spaces and define relative invariants for a pair $(X,\Sigma)$ consisting of a smooth, closed, oriented 4-manifold $X$ and a smooth, closed, oriented 2-dimensional submanifold $\Sigma\!\subset\!X$ with…
We completely determine the mod $2$ Seiberg-Witten invariants for any spin structure on any closed, oriented, smooth $4$-manifold $X$. Our computation confirms the validity of the simple type conjecture mod $2$ for spin structures. Our…
We develop an equivariant version of Seiberg-Witten-Floer cohomology for finite group actions on rational homology $3$-spheres. Our construction is based on an equivariant version of the Seiberg-Witten-Floer stable homotopy type, as…
The main theorem describes the behaviour of the stable cohomotopy invariant defined in the first article (joint with M. Furuta) in this series of two under the operation of taking connected sums of four-manifolds: The invariant of a…
In the second of a pair of papers, we complete the construction of Seiberg-Witten-like invariants for smooth four-manifolds equipped with broken fibrations, prove an index formula, and compute some examples.
Starting from ideas of Furuta, we develop a general formalism for the construction of cohomotopy invariants associated with a certain class of $S^1$-equivariant non-linear maps between Hilbert bundles. Applied to the Seiberg-Witten map,…
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'…
A compact oriented 4-manifold is defined to be of ``superconformal simple type'' if certain polynomials in the basic classes (constructed using the Seiberg-Witten invariants) vanish identically. We show that all known 4-manifolds of…
When a cyclic group G of prime order acts on a 4-manifold X, we prove a formula which relates the Seiberg-Witten invariants of X to those of X/G.
We construct examples of four dimensional manifolds with Spin$^c$-structures, whose moduli spaces of solutions to the Seiberg-Witten equations, represent a non-trivial bordism class of positive dimension, i.e. the Spin$^c$-structures are…
We consider several differential-topological invariants of compact 4-manifolds which directly arise from Riemannian variational problems. Using recent results of Bauer and Furuta, we compute these invariants in many cases that were…
Let $M$ be a closed oriented $4$-manifold admitting a rank-$2$ oriented foliation with a metric of leafwise positive scalar curvature. If $b^+>1$, then we will show that the Seiberg-Witten invariant vanishes for all \spinc structures.
We prove a conjecture of Hutchings and Lee relating the Seiberg-Witten invariants of a closed 3-manifold X with b_1 > 0 to an invariant that `counts' gradient flow lines--including closed orbits--of a circle-valued Morse function on the…
Let $X$ be a smooth, compact, oriented $4$-manifold. Building upon work of Li-Liu, Ruberman, Nakamura and Konno, we consider a families version of Seiberg-Witten theory and obtain obstructions to the existence of certain group actions on…
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…