Geometric structure and Floer theory of three-dimensional manifolds

三维流形的几何结构与Floer理论

• 批准号: RGPIN-2017-05440
• 负责人: Watson, Liam
• 金额: $ 2.55万
• 依托单位: Université de Sherbrooke
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635480
• 关键词: Geometric; structure; Floer; theory; three

Low-dimensional topology continues to draw on groundbreaking ideas of Floer. This has generated a vibrant sub-discipline; new structure is being uncovered and difficult problems are being solved. This activity comes alongside landmark achievements in geometric topology - e.g. Agol and Wise’s resolution of the virtual Haken conjecture - highlighting successes of Thurston’s program. My proposal is positioned at the nexus of these areas of activity, with a view to bridging between Thurston-style geometric topology and Floer-theoretic invariants in low-dimensions.

低维拓扑继续借鉴Floer的突破性思想。这产生了一个充满活力的分支学科;新的结构正在被发现，困难的问题正在被解决。这项活动伴随着几何拓扑学的里程碑式成就-例如Agol和Wise对虚哈肯猜想的解决-突出了Thurston计划的成功。我的建议是定位在这些领域的活动的联系，以期在瑟斯顿式的几何拓扑和Floer理论的不变量在低维之间的桥梁。