Mathematical Sciences: Free Loop Space, Automorphisms of Manifolds and Cyclic Homology

数学科学：自由循环空间、流形自同构和循环同调

• 批准号: 8917914
• 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: Continuing grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-02-01 至 1994-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8917914&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Free; Loop; Space

Professor Burghelea will study the topological character of natural transformations of simple geometric objects known as compact smooth manifolds. These arise in modern physical theories as well as in many purely mathematical contexts. Other related matters will also play a lesser role in his project. Specifically, Burghelea will study (1) the homotopy type of diffeomorphisms (resp. symplectomorphisms) of a compact smooth (resp. symplectic) manifold M and the relation to the homology of some associated spaces defined in terms of principal bundles over M. (2) the differential geometry and topology of the free loop space of compact Riemannian manifolds. (3) the determinants of elliptic operators. (4) the bounded concordances of complete metric manifolds. (5) geometric and algebraic problems in cyclic homology.

Burghelea教授将研究简单几何对象的自然转化的拓扑特征，称为紧凑的光滑歧管。 这些出现在现代物理理论以及许多纯粹的数学环境中。 其他相关事项也将在他的项目中扮演较少的角色。 具体而言，Burghelea将研究（1）紧凑的光滑（互置）歧管M的差异性（分别符号切除型）的同喻类型，以及与M.（2）紧凑型liopant sanfical Space sanemants the Princeplles decolts的某些相关空间的同源性关系的关系。 （3）椭圆运算符的决定因素。 （4）完整度量歧管的有界一致性。 （5）循环同源性中的几何和代数问题。