Maximal tori in the symplectomorphism groups of Hirzebruch surfaces
英文摘要:
We count the conjugacy classes of maximal tori in the groups of symplectomorphisms of S^2 \times S^2 and of the blow-up of CP^2 at a point.
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。
Yael Karshon
We count the conjugacy classes of maximal tori in the groups of symplectomorphisms of S^2 \times S^2 and of the blow-up of CP^2 at a point.
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
In a recent preprint Yael Karshon showed that there exist non-conjugate tori in a group of symplectomorphisms of a Hirzebruch surface. She counted them in terms of the cohomology class of the symplectic structure. We show that a similar phenomenon exists in the contactomorphism groups of pre-quantum circle bundles over Hirzebruch surfaces. Note that the contact structures in question are fillable. This may be contrasted with an earlier paper where we showed that there are infinitely many non-conjugate tori in the contactomorphism groups of certain overtwisted lens spaces (Contact cuts, Israel …
We show that compact toric cosymplectic manifolds are mapping tori of equivariant symplectomorphisms of toric symplectic manifolds.
This paper is concerned with the rational symplectic field theory in the Floer case. For this observe that in the general geometric setup for symplectic field theory the contact manifolds can be replaced by mapping tori of symplectic manifolds with symplectomorphisms. While the cylindrical contact homology is given by the Floer homologies of powers of the symplectomorphism, the other algebraic invariants of symplectic field theory provide natural generalizations of symplectic Floer homology. For symplectically aspherical manifolds and Hamiltonian symplectomorphisms we study the moduli spaces o…
In this paper, we describe explicit relations in the symplectomorphism groups of toric hypersurfaces. To define the elements involved, we construct a proper stack of toric hypersurfaces with compactifying boundary representing toric hypersurface degenerations. Our relations arise through the study of the one dimensional strata of this stack. The results are then examined from the perspective of homological mirror symmetry where we view sequences of relations as maximal degenerations of Landau-Ginzburg models. We then study the B-model mirror to these degenerations, which gives a new mirror sym…
By a theorem of Banyaga the group of diffeomorphisms of a manifold $P$ preserving a regular contact form $α$ is a central $S^1$ extension of the commutator of the group of symplectomorphisms of the base $B = P/S^1$. We show that if $T$ is a Hamiltonian maximal torus in the group of symplectomorphism of $B$, then its preimage under the extension map is a maximal torus not only in the group $\Diff(P, α)$ of diffeomorphisms of $P$ preserving $α$ but also in the much bigger group of contactomorphisms $\Diff (P, ξ)$, the group of diffeomorphism of $P$ preserving the contact distribution $ξ= \ker α$…
Centralizers of Hamiltonian circle actions on rational ruled surfaces
本文研究两类有理直纹面上 Hamilton $S^1$ 作用的等变辛微分同胚群,通过近复结构分层及 Delzant、Karshon 分类确定其同伦型为环面或两环面的同伦推出。
Product Lagrangian tori in standard symplectic space $R^{2n}$ were classified up to symplectomorphism in [Che96]. We extend this classification to tame symplectically aspherical symplectic manifolds. We show by examples that the asphericity assumption cannot be omitted.
By a result of Kedra and Pinsonnault, we know that the topology of groups of symplectomorphisms of symplectic 4-manifolds is complicated in general. However, in all known (very specific) examples, the rational cohomology rings of symplectomorphism groups are finitely generated. In this paper, we compute the rational homotopy Lie algebra of symplectomorphism groups of the 3-point blow-up of the projective plane (with an arbitrary symplectic form) and show that in some cases, depending on the sizes of the blow-ups, it is infinite dimensional. Moreover, we explain how the topology is generated by…
Hirzebruch surfaces provide an excellent example to underline the fact that in general symplectic manifolds, Gromov-Witten invariants might well count curves in the boundary components of the moduli space. We use this example to explain in detail that the counting argument given by Batyrev in "Quantum cohomology rings of toric manifolds" (Asterisque 218:9-34, 1993) does not work.
In this article, using the idea of toric degeneration and the computation of the full potential function of Hirzebruch surface $F_2$, which is \emph{not} Fano, we produce a continuum of Lagrangian tori in $S^2 \times S^2$ which are non-displaceable under the Hamiltonian isotopy.
Unobstructed embeddings in Hirzebruch surfaces
本文利用几乎环面纤维化在递归定义的无理参数值处构造Hirzebruch曲面的完全填充,证明这些值为无限阶梯的潜在值,为后续证明例外类与无限阶梯奠定基础。
We construct almost toric fibrations (ATFs) on all del Pezzo surfaces, endowed with a monotone symplectic form. Except for $\mathbb{C}P^2 \# 1 \overline{\mathbb{C}P^2}$ and $\mathbb{C}P^2 \# 2 \overline{\mathbb{C}P^2}$ , we are able to get almost toric base diagrams (ATBDs) of triangular shape and prove the existence of infinitely many symplectomorphism (in particular Hamiltonian isotopy) classes of monotone Lagrangian tori in $\mathbb{C}P^2 \# k \overline{\mathbb{C}P^2}$, for k=0,3,4,5,6,7,8. We name these tori $Θ^{n_1,n_2,n_3}_{p,q,r}$. Using the work of Karpov-Nogin, we are able to classify…
We prove that the group of Hamiltonian automorphisms of a symplectic 4-manifold contains only finitely many conjugacy classes of maximal compact tori with respect to the action of the full symplectomorphism group. We also extend to rational and ruled manifolds a result of Kedra which asserts that, if $M$ is a simply connected symplectic 4-manifold with $b_{2}\geq 3$, and if $\widetilde{M}_δ$ denotes a blow-up of $M$ of small enough capacity $δ$, then the rational cohomology algebra of the Hamiltonian group of $\widetilde{M}_δ)$ is not finitely generated. Both results are based on the fact that…
SYZ mirror of Hirzebruch surface $\mathbb{F}_k$ and Morse homotopy
本文利用Strominger-Yau-Zaslow镜像对构造和Morse同伦,将Hirzebruch曲面 $\mathbb{F}_1$ 的同调镜像对称性推广到 $\mathbb{F}_k$。
The spread construction and non-uniqueness of visible Lagrangians
研究 Hirzebruch 曲面中可见拉格朗日量的性质,通过新的展开构造证明其包含拉格朗日环面和克莱因瓶,且其拓扑不由矩映射像决定。
Staircase symmetries in Hirzebruch surfaces
本文继续研究 Hirzebruch 曲面族中的阶梯结构,揭示了允许阶梯存在的 b 集合背后的对称性及其与 Diophantine 方程的联系,并利用累积函数的算术性质简化了阶梯证明技术。
On Lagrangian Tori in $S^2\times S^2$
本文对 FOOO 构造的 $S^2\times S^2$ 中的环面纤维进行了全面分类,判断其是否与标准环面结构的纤维哈密顿同痕。
On SYZ mirrors of Hirzebruch surfaces
本文研究Hirzebruch面F_3和F_4的SYZ镜像对称性,通过正则化方法确定镜像超势能,并利用散射图联系不同扰动下的超势能。
Staircase Patterns in Hirzebruch Surfaces
本文近乎完整地描述了辛 Hirzebruch 曲面 H_b 椭球容量函数中的阶梯模式,利用几乎环面纤维化方法揭示了参数 b 的阻塞区间与存在阶梯的不可数取值,并证明了非特殊有理参数下的阶梯具有无理聚点。
A classification of infinite staircases for Hirzebruch surfaces
本文完成对复射影平面单点吹胀(Hirzebruch 曲面)嵌入函数无限阶梯的分类,证明有理权重下无限阶梯仅出现在权重为 1/3 时,并给出存在性的充分必要条件。
Centralizers of Hamiltonian finite cyclic group actions on rational ruled surfaces
本文研究有理直纹面上哈密顿有限循环群作用的等变辛微分同胚群的同伦型,证明满足特定条件的作用可延拓为环面作用,中心化子同伦等价于有限维李群或两环面沿圆周的同伦推出,依赖多种分类结果与全纯技术。
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。