Topology of positively curved manifolds with symmetry

• Applicant: Professor Dr. Anand Dessai
• Subject Area: Mathematics
• Term: from 2003 to 2007
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5406994

This project fits into the general framework of understanding topological features of positive curvature. Whereas topological consequences of positive scalar curvature are well understood only little is known for stronger notions such as positive Ricci or positive sectional curvature. Under weak symmetry assumptions index theoretical obstructions to positive sectional curvature can be formulated in terms of elliptic genera. The main aim of this project is to further explore relations between curvature properties and the theory of elliptic genera. One objective is to describe index theoretical obstructions for manifolds of positive kth Ricci curvature and symmetry. Also the classification of low dimensional manifolds of positive sectional curvature shall be pursued under weak symmetry assumption. Another aim of this project lies in the study of the geometry of string manifolds. Here the main focus is on the question whether the kernel of the Witten genus can be represented by string manifolds of positive Ricci curvature.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1154: Global Differential Geometry
• International Connection: Switzerland