ﻻ يوجد ملخص باللغة العربية
We show that the moduli space of regular affine vortices, which are solutions of the symplectic vortex equation over the complex plane, has the structure of a smooth manifold. The construction uses Zilteners Fredholm theory results [31]. We also extend the result to the case of affine vortices over the upper half plane. These results are necessary ingredients in defining the open quantum Kirwan map proposed by Woodward [24].
We construct a gluing map for stable affine vortices over the upper half plane with the Lagrangian boundary condition at a rigid, regular, codimension one configuration. This construction plays an important role in establishing the relation between t
The moduli space of flat SU(2) connections on a punctured surface, having prescribed holonomy around the punctures, is a compact smooth manifold if the prescription is generic. This paper gives a direct, elementary proof that the trace of the holonom
We consider deformations of torsion-free G2 structures, defined by the G2-invariant 3-form $phi$ and compute the expansion of the Hodge star of $phi$ to fourth order in the deformations of $phi$. By considering M-theory compactified on a G2 manifold,
The dynamics of both global and local vortices with non-Abelian orientational moduli is investigated in detail. Head-on collisions of these vortices are numerically simulated for parallel, anti-parallel and orthogonal internal orientations where we f
In this article we study Weinstein structures endowed with a Lefschetz fibration in terms of the Legendrian front projection. First we provide a systematic recipe for translating from a Weinstein Lefschetz bifibration to a Legendrian handlebody. Then