Poisson Fibrations and Fibered Symplectic Groupoids
英文摘要:
We show that Poisson fibrations integrate to a special kind of symplectic fibrations, called fibered symplectic groupoids.
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。
Olivier Brahic, Rui Loja Fernandes
We show that Poisson fibrations integrate to a special kind of symplectic fibrations, called fibered symplectic groupoids.
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
As groupoids generalize groups, motivated by group extensions we consider a kind of fibrations of Lie groupoids, called locally topological product Lie groupoid fibrations with fiber $\sf A$, i.e., \[ 1\rightarrow {\sf A} \rightarrow {\sf G} \rightarrow {\sf K}\rightarrow 1 \] where $\sf A,\sf G$ and $\sf K$ are Lie groupoids. Similar to the theory of group extensions, we show that the existence of locally topological product Lie groupoid fibrations with fiber $\sf A$ over $\sf K$ is obstructed by a groupoid cohomology of $H^3_{\bar Λ}({\sf K},Z_{\sf A})$, and these locally topological product…
In this paper, we generalize the notion of Serre fibration to the Morita category of topological groupoids and derive the associated long exact sequence of homotopy groups. We use this results for calculation of homotopy groups of various groupoids, such as the foliation groupoid of a Riemannian foliation.
Multiplicative Ehresmann connections for Lie groupoid fibrations
本文研究了李群oids纤维化的乘法Ehresmann连接,探讨了其存在性及完备性,指出在特定条件下此类连接的存在与基连接和核束连接相关联。
Automorphisms of Lie groupoids and symplectic reduction on orbifolds
本文研究了李群体的自同构2-群BAut(X)以及其在orbifold上的辛约简,通过Kan纤维化理论建立了2-群作用与李群体的等价关系,并探讨了辛约简的性质和应用。
Let $\mathcal{G} \rightrightarrows M$ be a source locally trivial proper Lie groupoid such that each orbit is of finite type. The orbit projection $M \to M/\mathcal{G}$ is a fibration if and only if $\mathcal{G} \rightrightarrows M$ is regular.
In this thesis, we employ simplicial methods to study actions, principal bundles, and bibundles of higher groupoids. Roughly, we use Kan fibrations to model actions of higher groupoids, we use pairs of a Kan fibration and a special acyclic fibration to model principal bundles of higher groupoids, we use inner Kan fibrations over the interval to model bibundles of higher groupoids. In particular, we show that our definitions given by the simplicial method agree with those given by the categorification approach to actions, principal bundles, and bibundles of 2-groupoids. In addition, we use the …
In this note we show that if a compact Kahler manifold with trivial canonical bundle is the total space of a holomorphic fibration without singular fibers, then the fibration is a holomorphic fiber bundle. In the algebraic case, the fibration becomes trivial after a finite base change.
Lie $\infty$-groupoids are simplicial Banach manifolds that satisfy an analog of the Kan condition for simplicial sets. An explicit construction of Henriques produces certain Lie $\infty$-groupoids called `Lie $\infty$-groups' by integrating finite type Lie $n$-algebras. In order to study the compatibility between this integration procedure and the homotopy theory of Lie $n$-algebras introduced in the companion paper arXiv:1809.05999, we present a homotopy theory for Lie $\infty$-groupoids. Unlike Kan simplicial sets and the higher geometric groupoids of Behrend and Getzler, Lie $\infty$-group…
We introduce in this paper a field theory on symplectic manifolds that are fibered over a real surface with interior marked points and cylindrical ends. We assign to each such object a morphism between certain tensor products of quantum and Floer homologies that are canonically attached to the fibration. We prove a composition theorem in the spirit of QFT, and show that this field theory applies naturally to the problem of minimising geodesics in Hofer's geometry. This work can be considered as a natural framework that incorporates both the Piunikhin-Salamon-Schwarz morphisms and the Seidel is…
Complete Calabi-Yau metrics on noncompact abelian fibered threefolds
研究以 $\mathbb{C}$ 为底的非紧阿贝尔纤维化三维流形,构造其上的完备 Calabi-Yau 度量,并给出典范丛为负的紧化。
We describe pairs (p,n) such that n-dimensional affine space is fibered by pairwise skew p-dimensional affine subspaces. The problem is closely related with the theorem of Adams on vector fields on spheres and the Hurwitz-Radon theory of composition of quadratic forms.
We study Riemannian metrics on Lie groupoids in the relative setting. We show that any split fibration between proper groupoids can be made Riemannian, and we use these metrics to linearize proper groupoid fibrations. As an application, we derive rigidity theorems for Lie groupoids, which unify, simplify and improve similar results for classic geometries. Then we establish the Morita invariance for our metrics, introduce a notion for metrics on stacks, and use them to construct stacky tubular neighborhoods and to prove a stacky Ehresmann theorem.
Hyper-Kähler Fourfolds Fibered by Elliptic Products
本文研究射影超凯勒四流形中以两条椭圆曲线乘积为纤维的纤维化,在温和一般性条件下补充了Markushevich对雅可比簇情形的分类。
In this paper we consider a family of Dirac-type operators on fibration $P \to B$ equivariant with respect to an action of an etale groupoid. Such a family defines an element in the bivariant $K$ theory. We compute the action of the bivariant Chern character of this element on the image of Connes' map $Φ$ in the cyclic cohomology. A particular case of this result is Connes' index theorem for etale groupoids in the case of fibrations.
We establish constraints on the topology of smooth Lefschetz fibrations with $4$-dimensional fibers, by studying the family Bauer-Furuta invariant. To compute this invariant, we analyze the framed bordism class of 1-dimensional Seiberg-Witten moduli spaces using the local index theorem by Bismut-Freed. Using this, we deduce new obstructions to the smooth isotopy to the identity for compositions of Dehn twists on $(-2)$-spheres in closed $4$-manifolds. We obtain several applications: (1) We exhibit the first examples of closed simply-connected symplectic $4$-manifolds admitting Torelli symplect…
扫码添加微信好友,提出您的宝贵建议 👇
💡 备注请填写:网站反馈
发表机构由 AI 从论文文本抽取,如发现错误,欢迎反馈修正建议。