Topological aspects of symplectic manifolds with symmetries (A01)

具有对称性的辛流形的拓扑方面（A01）

• 批准号: 330778469
• 金额: --
• 依托单位: Abteilung Mathematik
• 依托单位国家: 德国
• 项目类别: CRC/Transregios
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/330778469?language=en
• 关键词: Topological; aspects; symplectic; manifolds; symmetries

We continue and expand our study of topological properties of symplectic and Kähler manifolds endowed with a compact Lie group action, aiming at information on their equivariant topological invariants. Key objects of study are compact symplectic manifolds with a torus action, and manifolds associated with representations of quivers. More specifically, we will study the topological invariants and diffeomorphism type of compact symplectic manifolds of dimension 6 with a Hamiltonian action of a 2-torus, which goes in the direction of proving a conjecture posed by Fine and Panov, and we will study the Mukai inequality for certain categories of monotone manifolds, using new techniques developed during the first funding period. Moreover, we will continue the development of a GKM type theory for moduli spaces of quiver representations, with applications to Donaldson-Thomas and Gromov-Witten invariants.

我们继续并扩展了具有紧李群作用的辛流形和Kähler流形的拓扑性质，旨在获得它们的等变拓扑不变量的信息。研究的主要对象是具有环面作用的紧辛流形和与颤振表示相关的流形。更具体地说，我们将研究具有2环面哈密顿作用的6维紧辛流形的拓扑不变量和微分同构类型，这将朝着证明Fine和Panov提出的一个猜想的方向发展，我们将研究某些类别单调流形的Mukai不等式，使用第一个资助期间开发的新技术。此外，我们将继续发展颤模空间的GKM型理论，并将其应用于Donaldson-Thomas和Gromov-Witten不变量。