2 problems

Group-ring resolution conjecture. There is a function $f(n)$ such that every $n$-generated ideal in $\mathbb K[G]$ has a free resolution of length $r-1$.

Let $X$ be an $n$-dimensional Riemannian manifold with sectional curvature $K\geq 1$, and let $f:X\to\mathbb{R}^k$ be a continuous map. For a subset $Y\subset X$, write…