Positive Curvature and F_0-Spaces

• Applicant: Privatdozent Dr. Manuel Amann
• Subject Area: Mathematics
• Term: from 2010 to 2012
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 181716706

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).

• DFG Programme: Research Fellowships
• International Connection: Canada
• Host: Professor Dr. Vitali Kapovich