Positive Curvature and F_0-Spaces

正曲率和 F_0 空间

• 批准号: 181716706
• 负责人: Privatdozent Dr. Manuel Amann
• 金额: --
• 依托单位: Lehrstuhl für Differentialgeometrie
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2011-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/181716706?language=en
• 关键词: Positive; Curvature; F_0; Spaces

Conjecturally, from the viewpoint of Rational Homotopy Theory, even-dimensional Riemannian manifolds with positive sectional curvature have the structure of an F_0-space, i. e. a rationally elliptic space with positive Euler characteristic. On the one hand I intend to investigate (rationally elliptic) Riemannian manifolds with positive/non-negative curvature under the assumption of isometric torus actions via an approach by equivariant Rational Homotopy Theory. On the other hand I plan to derive further properties of F_0-spaces, more concretely, to establish for example the Halperin conjecture for certain classes of F_0-spaces. I shall study this conjecture on manifolds with symmetry and on further special classes of manifolds like biquotients (among which almost all the known examples of manifolds with positive curvature can be found).

从有理同伦理论的观点出发，我们猜想具有正截面曲率的偶数维黎曼流形具有F_0-空间的结构，即：e.具有正欧拉特征的有理椭圆空间。一方面，我打算通过等变有理同伦理论的方法，在等距环面作用的假设下，研究（有理椭圆）具有正/非负曲率的黎曼流形。另一方面，我计划得到进一步的性质的F_0-空间，更具体地说，建立例如Halperin猜想某些类的F_0-空间。我将研究这一猜想的流形与对称性和进一步特殊类的流形一样bipolitents（其中几乎所有已知的例子流形正曲率可以找到）。