A symplectic proof of Seiberg-Witten blow-up formula
نویسندگان
چکیده
In this paper, we give a symplectic proof for Seiberg-Witten blow-up formula of four dimensional symplectic manifolds, especially we interpret a strange phenomenon that the genera of embedding J-holomorphic curves will decrease when we symplectically blow-up the four dimensional symplectic manifold.
منابع مشابه
Removable singularities and a vanishing theorem for Seiberg-Witten invariants
This result is the Seiberg-Witten analogue of Donaldson’s original theorem about the vanishing of the instanton invariants [2] for connected sums. An outline of the proof of Theorem 1.1 was given by Donaldson in [1]. The key ingredient of the proof is a removable singularity theorem for the Seiberg-Witten equations on flat Euclidean 4-space. A proof of Theorem 1.1 was also indicated by Witten i...
متن کاملGromov-Witten Invariants of Blow-ups Along Points and Curves
In this paper, usng the gluing formula of Gromov-Witten invariants under symplectic cutting, due to Li and Ruan, we studied the Gromov-Witten invariants of blow-ups at a smooth point or along a smooth curve. We established some relations between Gromov-Witten invariants of M and its blow-ups at a smooth point or along a smooth curve.
متن کاملSymplectic Fibrations and the Abelian Vortex Equations
The nth symmetric product of a Riemann surface carries a natural family of Kähler forms, arising from its interpretation as a moduli space of abelian vortices. We give a new proof of a formula of Manton–Nasir [10] for the cohomology classes of these forms. Further, we show how these ideas generalise to families of Riemann surfaces. These results help to clarify a conjecture of D. Salamon [13] o...
متن کاملSW ⇒ Gr: FROM THE SEIBERG-WITTEN EQUATIONS TO PSEUDO-HOLOMORPHIC CURVES
The purpose of this article is to explain how pseudo-holomorphic curves in a symplectic 4-manifold can be constructed from solutions to the Seiberg-Witten equations. As such, the main theorem proved here (Theorem 1.3) is an existence theorem for pseudo-holomorphic curves. This article thus provides a proof of roughly half of the main theorem in the announcement [T1]. That theorem, Theorem 4.1, ...
متن کاملAn introduction to the Seiberg-Witten equations on symplectic manifolds∗
The Seiberg-Witten equations are defined on any smooth 4-manifold. By appropriately counting the solutions to the equations, one obtains smooth 4-manifold invariants. On a symplectic 4-manifold, these invariants have a symplectic interpretation, as a count of pseudoholomorphic curves. This allows us to transfer information between the smooth and symplectic categories in four dimensions. In the ...
متن کامل