Mathematical Sciences: Topics in Topology

数学科学：拓扑主题

• 批准号: 9501701
• 负责人: Dan Burghelea
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501701&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Topology

9501701 Burghelea This project pursues research on the topology of the free loop spaces, on the homotopy type of the space of symplectomorphisms and on von Neumann topology. More precisely, one investigates: (1) the analogy between algebraic topology of the free loop spaces and algebraic geometry; (2) applications of string cohomology; (3) new methods to detect nontrivial homotopy groups of the space of symplectomorphisms; and (4) numerical invariants such as the Novikov-Shubin invariant, L2-torsion, and the L2-eta invariant for compact manifolds with infinite fundamental group. This research will provide new developments in areas like algebraic geometry, differential geometry, elliptic operators, and von Neumann algebras. It will broaden the present knowledge in, and (hopefully) will discover new relationships between, such different areas as algebraic geometry and free loop spaces, or algebraic geometry and symplectotopology. It will also answer specific questions (solve ppoblems) of immediate concern in topology, geometry and mathematical physics. ***

小行星9501701 该项目致力于研究自由回路空间的拓扑结构、辛同伦空间的同伦类型和冯·诺依曼拓扑结构。 更确切地说，我们研究了：（1）自由圈空间的代数拓扑与代数几何之间的类比;（2）弦上同调的应用;（3）检测辛同胚空间的非平凡同伦群的新方法;以及（4）数值不变量，例如Novikov-Shubin不变量，L2-挠率，以及具有无限基本群的紧致流形的L2-eta不变量。 这项研究将提供新的发展领域，如代数几何，微分几何，椭圆算子，冯诺依曼代数。 它将扩大目前的知识，并（希望）将发现新的关系，这些不同的领域，如代数几何和自由循环空间，或代数几何和symplectopology。 它还将回答拓扑学，几何学和数学物理学中直接关注的特定问题（解决问题）。 ***