相关论文: Seiberg--Witten invariants and surface singulariti…
Assume that $M(\mathcal{T})$ is a rational homology sphere plumbed 3-manifold associated with a connected negative definite graph $\mathcal{T}$. We consider the combinatorial multivariable Poincar\'e series associated with $\mathcal{T}$ and…
In this article, for any Seifert fibered homology 3-sphere, we introduce homological blocks with simple Lie algebra and prove that its radial limits are identified with the Witten--Reshetikhin--Turaev invariants. To prove it, we develop an…
In these notes, we carefully analyze the properties of the "ramified" Seiberg-Witten equations associated with supersymmetric configurations of the Seiberg-Witten abelian gauge theory with surface operators on an oriented closed…
For every rational homology 3-sphere with 2-torsion only we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring), such that the evaluation of this invariant at any odd root of unity…
Let $(F,J,\omega)$ be an almost K\"ahler manifold, $\alpha$ a $J$-holomorphic action of a compact Lie group $\hat K$ on $F$, and $K$ a closed normal subgroup of $\hat K$ which leaves $\omega$ invariant. We introduce gauge theoretical…
Using lattice homology, we give an explicit combinatorial description of the Seiberg-Witten-Floer spectrum $\mathit{SWF}(Y)$ for $Y$ an almost-rational plumbed homology sphere. This class of manifolds includes all Seifert fibered rational…
We determine the local equivalence class of the Seiberg-Witten Floer stable homotopy type of a spin rational homology 3-sphere $Y$ embedded into a spin rational homology $S^{1} \times S^{3}$ with a positive scalar curvature metric so that…
We establish the exact triangle in Seiberg-Witten-Floer theory relating the monopoloe homologies of any two closed 3-manifolds which are obtained from each other by $\pm 1$-surgery. We also show that the sum of the modified version of the…
This expository talk is an expanded version of a lecture at G.-M. Greuel's 60th Birthday Conference in Kaiserslautern in October, 2004. We survey recent work of Neumann-Wahl and others on the relation between topology and geometry of normal…
This is a survey article on the stable cohomotopy refinement of Seiberg-Witten invariants containing also new results, for example: - Stable cohomotopy groups describe path components of certain mapping spaces. - Relation of stable…
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…
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 prove that the monodromy diffeomorphism of a complex 2-dimensional isolated hypersurface singularity of weighted-homogeneous type has infinite order in the smooth mapping class group of the Milnor fiber, provided the singularity is not a…
We show that the Witten-Reshetikhin-Turaev SU(2) invariant and the Hennings invariant associated to the restricted quantum $sl_2$ are essentially the same for rational homology 3-spheres.
R.~Lawrence has conjectured that for rational homology spheres, the series of Ohtsuki's invariants converges p-adicly to the SO(3) Witten-Reshetikhin-Turaev invariant. We prove this conjecture for Seifert rational homology spheres. We also…
The purpose of this note is to give a short, selfcontained proof of the following result: A complex surface which is diffeomeorphic to a rational surface is rational.
The purpose of this paper is: 1) to explain the Seiberg-Witten invariants, 2) to show that - on a K\"ahler surface - the solutions of the monopole equations can be interpreted as algebraic objects, namely effective divisors, 3) to give - 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…
We define Pin(2)-equivariant Seiberg-Witten Floer homology for rational homology 3-spheres equipped with a spin structure. The analogue of Froyshov's correction term in this setting is an integer-valued invariant of homology cobordism whose…
Meier and Zupan showed that every surface in the four-sphere admits a bridge trisection and can therefore be represented by three simple tangles. This raises the possibility of applying methods from link homology to knotted surfaces. We use…