Related papers: On integral rigidity in Seiberg-Witten theory

The main results of this paper describes a formula for the Seiberg-Witten invariant of a 4-manifold which admits a nontrivial free S^1-action. We use this theorem to produce a nonsymplectic 4-manifold with a free circle action whose orbit…

For any $s \in [-\infty, 0] $ and oriented homology 3-sphere $Y$, we introduce a homology cobordism invariant $r_s(Y)\in (0,\infty]$. The values $\{r_s(Y)\}$ are included in the critical values of the $SU(2)$-Chern-Simons functional of $Y$,…

The works of Donaldson and Mark make the structure of the Seiberg-Witten invariant of 3-manifolds clear. It corresponds to certain torsion type invariants counting flow lines and closed orbits of a gradient flow of a circle-valued Morse map…

This article analyzes the interplay between symplectic geometry in dimension four and the invariants for smooth four-manifolds constructed using holomorphic triangles introduced in math.SG/0110169. Specifically, we establish a non-vanishing…

This is the third paper of this series. In \cite{Wang20}, we defined the monopole Floer homology for any pair $(Y,\omega)$, where $Y$ is a compact oriented 3-manifold with toroidal boundary and $\omega$ is a suitable closed 2-form viewed as…

Under some suitable assumptions Riemannian manifolds $(M, g, H)$ that admit a connection $\hat\nabla$ with torsion a 3-form $H$, which is both closed $d H=0$ and $\hat\nabla$-covariantly constant, are locally isometric to a product $N\times…

We prove rigidity results describing contextually-constrained maps defined on Grassmannians and manifolds of ordered independent line tuples in finite-dimensional vector or Hilbert spaces. One statement in the spirit of the Fundamental…

We obtain the Seiberg-Witten geometry for four-dimensional N=2 gauge theory with gauge group SO(2N_c) (N_c \leq 5) with massive spinor and vector hypermultiplets by considering the gauge symmetry breaking in the N=2 $E_6$ theory with…

The Bauer-Furuta invariant of a family of smooth 4-manifolds is a stable cohomotopy refinement of the families Seiberg-Witten invariant and is constructed from a finite dimensional approximation of the Seiberg-Witten monopole map. We prove…

For each integer q>0 there is a cohomology theory such that the zero cohomology group of a manifold N of dimension n is a certain group of cobordism classes of proper fold maps of manifolds of dimension n+q into N. We prove a splitting…

Various Seiberg-Witten Floer cohomologies are defined for a closed, oriented 3-manifold; and if it is the mapping torus of an area-preserving surface automorphism, it has an associated periodic Floer homology as defined by Michael…

Noncommutative versions of theories with a gauge freedom define (when they exist) consistent deformations of their commutative counterparts. General aspects of Seiberg-Witten maps are discussed from this point of view. In particular, the…

For a given smooth $2$-knot in $S^4$, we relate the existence of a smooth Seifert hypersurface of a certain class to the existence of irreducible $ SU(2)$-representations of its knot group. For example, we see that any smooth $2$-knot…

We construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes…

In this paper we construct a Floer-homology invariant for a natural and wide class of sutured manifolds that we call balanced. This generalizes the Heegaard Floer hat theory of closed three-manifolds and links. Our invariant is unchanged…

We prove that homological stability fails for the moduli space of any simply-connected closed smooth 4-manifold in any degree of homology, unlike what happens in all dimensions $\neq 4$. We detect also the homological discrepancy between…

We demonstrate an obstruction to finding certain splittings of four-manifolds along sufficiently twisted circle bundles over Riemann surfaces, arising from Seiberg-Witten theory. These obstructions are used to show a non-splitting result…

We obtain new invariants of topological link concordance and homology cobordism of 3-manifolds from Hirzebruch-type intersection form defects of towers of iterated p-covers. Our invariants can extract geometric information from an arbitrary…

We prove an analogue of the Kotschick-Morgan conjecture in the context of SO(3) monopoles, obtaining a formula relating the Donaldson and Seiberg-Witten invariants of smooth four-manifolds using the SO(3)-monopole cobordism. The main…

We show that every positive definite closed 4-manifold with $b_2^+>1$ and without 1-handles has a vanishing stable cohomotopy Seiberg-Witten invariant, and thus admits no symplectic structure. We also show that every closed oriented…