ترغب بنشر مسار تعليمي؟ اضغط هنا

Deformations of symplectic vortices

120   0   0.0 ( 0 )
 نشر من قبل Chris T. Woodward
 تاريخ النشر 2010
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We prove a gluing theorem for a symplectic vortex on a compact complex curve and a collection of holomorphic sphere bubbles. Using the theorem we show that the moduli space of regular stable symplectic vortices on a fixed curve with varying markings has the structure of a stratified-smooth topological orbifold. In addition, we show that the moduli space has a non-canonical $C^1$-orbifold structure.



قيم البحث

اقرأ أيضاً

318 - Boris Khesin 2011
We present the Hamiltonian formalism for the Euler equation of symplectic fluids, introduce symplectic vorticity, and study related invariants. In particular, this allows one to extend D.Ebins long-time existence result for geodesics on the symplecto morphism group to metrics not necessarily compatible with the symplectic structure. We also study the dynamics of symplectic point vortices, describe their symmetry groups and integrability.
We describe the deformation cohomology of a symplectic groupoid, and use it to study deformations via Moser path methods, proving a symplectic groupoid version of the Moser Theorem. Our construction uses the deformation cohomologies of Lie groupoids and of multiplicative forms, and we prove that in the symplectic case, deformation cohomology of both the underlying groupoid and of the symplectic groupoid have de Rham models in terms of differential forms. We use the de Rham model, which is intimately connected to the Bott-Shulman-Stasheff double complex, to compute deformation cohomology in several examples. We compute it for proper symplectic groupoids using vanishing results; alternatively, for groupoids satisfying homological 2-connectedness conditions we compute it using a simple spectral sequence. Finally, without making assumptions on the topology, we constructed a map relating differentiable and deformation cohomology of the underlying Lie groupoid of a symplectic groupoid, and related it to its Lie algebroid counterpart via van Est maps.
387 - Claude Viterbo 2014
Let $H(q,p)$ be a Hamiltonian on $T^*T^n$. We show that the sequence $H_{k}(q,p)=H(kq,p)$ converges for the $gamma$ topology defined by the author, to $bar{H}(p)$. This is extended to the case where only some of the variables are homogenized, that is the sequence $H(kx,y,q,p)$ where the limit is of the type ${bar H}(y,q,p)$ and thus yields an effective Hamiltonian. We give here the proof of the convergence, and the first properties of the homogenization operator, and give some immediate consequences for solutions of Hamilton-Jacobi equations, construction of quasi-states, etc. We also prove that the function $bar H$ coincides with Mathers $alpha$ function which gives a new proof of its symplectic invariance proved by P. Bernard. A previous version of this paper relied on the former On the capacity of Lagrangians in $T^*T^n$ which has been withdrawn. The present version of Symplectic Homogenization does not rely on it anymore.
318 - Yael Karshon , Xiudi Tang 2021
We say that a subset of a symplectic manifold is symplectically (neighbourhood) excisable if its complement is symplectomorphic to the ambient manifold, (through a symplectomorphism that can be chosen to be the identity outside an arbitrarily small n eighbourhood of the subset). We use time-independent Hamiltonian flows, and their iterations, to show that certain properly embedded subsets of noncompact symplectic manifolds are symplectically neighbourhood excisable: a ray, a Cantor brush, a box with a tail, and -- more generally -- epigraphs of lower semi-continuous functions; as well as a ray with two horns, and -- more generally -- open-rooted finite trees.
We give characterizations of a finite group $G$ acting symplectically on a rational surface ($mathbb{C}P^2$ blown up at two or more points). In particular, we obtain a symplectic version of the dichotomy of $G$-conic bundles versus $G$-del Pezzo surf aces for the corresponding $G$-rational surfaces, analogous to a classical result in algebraic geometry. Besides the characterizations of the group $G$ (which is completely determined for the case of $mathbb{C}P^2# Noverline{mathbb{C}P^2}$, $N=2,3,4$), we also investigate the equivariant symplectic minimality and equivariant symplectic cone of a given $G$-rational surface.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا