Cohomology of Symmetric Spaces as seen from Infinity

• Applicants: Professor Dr. Tobias Hartnick; Privatdozent Dr. Andreas Ott
• Subject Area: Mathematics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 441895682

The isomorphism conjecture in continuous bounded cohomology predicts that the cohomology of a symmetric space of compact type can be recovered from the geometry at infinity of its non-compact dual symmetric space by taking the cohomology of the complex of invariant bounded measurable functions on products of Furstenberg boundaries. The goal of this project is to establish several special cases of the conjecture. On the one hand we focus on general vanishing theorems which would follow from the conjecture, and on the other hand we aim to establish qualitative results in the vein of cohomological stability.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2026: Geometry at Infinity
• International Connection: Israel
• Cooperation Partner: Dr. Carlos De la Cruz Mengual