Positive Curvature and F_0-Spaces

• Antragsteller: Privatdozent Dr. Manuel Amann
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2010 bis 2012
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 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-Verfahren: Forschungsstipendien
• Internationaler Bezug: Kanada
• Gastgeber: Professor Dr. Vitali Kapovich