Simplicial Volume and Bounded Cohomology (B05)

该项目旨在更好地从计算和结构上理解简单体积和有界上同。主要的挑战是简单体积不是一个可计算的不变量和有界上同调不满足切除。在前一个资助期的基础上，我们将结合特殊情况下的直接几何和上同调计算，通过遍历理论的近似结果和绝对刚性，以及来自高等范畴理论的工具。

This project aims at a better computational and structural understanding of simplicial volume and bounded cohomology. The main challenges are that simplicial volume is not a computable invariant and that bounded cohomology does not satisfy excision. Building on the progress of the previous funding periods, we will combine direct geometric and cohomological computations in special cases, approximation results and profinite rigidity via ergodic theory, and tools from higher category theory.