arXiv math/01102852001-10math.SG

Grafting Seiberg-Witten monopoles

Stanislav Jabuka

备注：: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-7.abs.html
发表信息：: Algebr. Geom. Topol. 3 (2003) 155-185
DOI：: 10.2140/agt.2003.3.155

英文摘要：

We demonstrate that the operation of taking disjoint unions of J-holomorphic curves (and thus obtaining new J-holomorphic curves) has a Seiberg-Witten counterpart. The main theorem asserts that, given two solutions (A_i, psi_i), i=0,1 of the Seiberg-Witten equations for the Spin^c-structure W^+_{E_i}= E_i direct sum (E_i tensor K^{-1}) (with certain restrictions), there is a solution (A, psi) of the Seiberg-Witten equations for the Spin^c-structure W_E with E= E_0 tensor E_1, obtained by `grafting' the two solutions (A_i, psi_i).

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

The absolute gradings on embedded contact homology and Seiberg-Witten Floer cohomology

Let Y be a closed connected contact 3-manifold. In the series of papers "Embedded contact homology and Seiberg-Witten Floer cohomology I-V", Taubes defines an isomorphism between the embedded contact homology (ECH) of Y and its Seiberg-Witten Floer cohomology. Both the ECH of Y and the Seiberg-Witten Floer cohomology of Y admit absolute gradings by homotopy classes of oriented two-plane fields. We show that Taubes' isomorphism preserves these gradings. To do this, we prove another result relating the expected dimension of any component of the Seiberg-Witten moduli space over a completed connec…

2013-03-13math.SG

HF=HM V: Seiberg-Witten-Floer homology and handle addition

This is the last of five papers that construct an isomorphism between the Seiberg-Witten Floer homology and the Heegaard Floer homology of a given compact, oriented 3-manifold.

2017-09-08math.GTmath.SG

Embedded contact homology and Seiberg-Witten Floer cohomology I

This is the first of five papers that construct an isomorphism between the embedded contact homology and Seiberg-Witten Floer cohomology of a compact 3-manifold with a given contact 1-form. This paper describes what is involved in the construction.

2008-12-04math.GTmath.SG

Periodic Floer homology and Seiberg-Witten Floer cohomology

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 Hutchings. We construct an isomorphism between a certain version of Seiberg-Witten Floer cohomology and the corresponding periodic Floer homology, and describe some immediate consequences.

2011-05-23math.GTmath.SG

Relative Seiberg-Witten and Ozsvath-Szabo 4-dimensional invariants with respect to embedded surfaces

We study the invariants of surfaces in 4-manifolds extracted from the Seiberg-Witten and the Ozsvath-Szabo invariants of their fiber sums with auxiliary Lefschetz fibrations. Such invariants involve relative Spin_c structures and can be treated as refinements of the usual Seiberg-Witten and Ozsvath-Szabo invariants. We prove for instance the adjunction inequality for membranes, which estimates their genus.

2005-07-14math.GTmath.SG

Family Seiberg-Witten invariants and wall crossing formulas

In this paper we set up the family Seiberg-Witten theory. It can be applied to the counting of nodal pseudo-holomorphic curves in a symplectic 4-manifold (especially a Kahler surface). A new feature in this theory is that the chamber structure plays a more prominent role. We derive some wall crossing formulas measuring how the family Seiberg-Witten invariants change from one chamber to another.

2001-08-31math.GTmath.SG

更多相关论文收起更多论文

HF=HM IV: The Seiberg-Witten Floer homology and ech correspondence

This is the fourth of five papers that construct an isomorphism between the Seiberg-Witten Floer homology and the Heegaard Floer homology of a given compact, oriented 3-manifold. The isomorphism is given as a composition of three isomorphisms; the first of these relates a version of embedded contact homology on an an auxillary manifold to the Heegaard Floer homology on the original. The second isomorphism relates the relevant version of the embedded contact homology on the auxilliary manifold with a version of the Seiberg-Witten Floer homology on this same manifold. The third isomorphism relat…

2011-07-12math.GTmath.SG

On the Riemannian geometry of Seiberg-Witten moduli spaces

We construct natural Riemannian metrics on Seiberg-Witten moduli spaces and study their geometry.

2008-03-19math-phmath.DGmath.MP

Nondiffeomorphic symplectic 4-manifolds with the same Seiberg-Witten invariants

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.

1999-11-17math.GTmath.SG

A symplectic proof of Seiberg-Witten blow-up formula

withdrawn by authors

2009-01-07math.AGmath.DGmath.SG

Symplectic mapping class groups of K3 surfaces and Seiberg-Witten invariants

The purpose of this note is to prove that the symplectic mapping class groups of many K3 surfaces are infinitely generated. Our proof makes no use of any Floer-theoretic machinery but instead follows the approach of Kronheimer and uses invariants derived from the Seiberg-Witten equations.

2022-02-09math.DGmath.SG

HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology

Let M be a closed, connected and oriented 3-manifold. This article is the first of a five part series that constructs an isomorphism between the Heegaard Floer homology groups of M and the corresponding Seiberg-Witten Floer homology groups of M.

2011-07-12math.GTmath.SG

Seiberg-Witten invariants and real curves

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' results, we prove that on a symplectic almost complex manifold with an antisymplectic and antiholomorphic involution, this invariants are not all trivial, and that the canonical bundle is represented by a real holomorphic curve.

2004-04-30math.CVmath.DGmath.SG

Intersection theory of coassociative submanifolds in G_(2)-manifolds and Seiberg-Witten invariants

We study the problem of counting instantons with coassociative boundary condition in (almost) G_(2)-manifolds. This is analog to the open Gromov-Witten theory for counting holomorphic curves with Lagrangian boundary condition in Calabi-Yau manifolds. We explain its relationship with the Seiberg-Witten invariants for coassociative submanifolds.

2004-01-29math-phmath.DGmath.MP

Heegaard Splittings and Seiberg-Witten monopoles

This is an expansion on my talk at the Geometry and Topology conference at McMaster University, May 2004. We outline a program to relate the Heegaard Floer homologies of Ozsvath-Szabo, and Seiberg-Witten-Floer homologies as defined by Kronheimer-Mrowka. The center-piece of this program is the construction of an intermediate version of Floer theory, which exhibits characteristics of both theories.

2004-10-06math.DGmath.GTmath.SG

Thin instantons in G_2-manifolds and Seiberg-Witten invariants

For two nearby disjoint coassociative submanifolds C and C' in a G_2-manifold, we construct thin instantons with boundaries lying on C and C' from regular J-holomorphic curves in C. We explain their relationship with the Seiberg-Witten invariants for C.

2013-03-27math-phmath.DGmath.MP