Asymptotic Invariants of Manifolds

流形的渐近不变量

• 批准号: 5453729
• 负责人: Professor Dieter Kotschick, Ph.D.
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2005
• 资助国家: 德国
• 起止时间: 2004-12-31 至 2011-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5453729?language=en
• 关键词: Asymptotic; Invariants; Manifolds

We investigate several asymptotic invariants of closed manifolds which are related to the minimal volume entropy, with special emphasis on the isoperimetric constant, the minimal eigenvalue, the spherical volume, and the systolic constant. We study the behaviour of these invariants under homotopy equivalence, under homeomorphism and under bordism. We prove inequalities between these invariants and we consider applications to geometric problems in which asymptotic invariants appear naturally.

我们研究了与最小体积熵相关的闭流形的几个渐近不变量，特别强调等周常数、最小特征值、球体积和收缩常数。我们研究这些不变量在同伦等价、同胚和边对称下的行为。我们证明了这些不变量之间的不等式，并考虑了在渐近不变量自然出现的几何问题中的应用。