2 problems

Let $M$ be a closed oriented Riemannian manifold with a non-zero relevant topological invariant, and let $D=\{(x_+,+1),(x_-,-1)\}$ consist of two oppositely labelled points at geod…

Let $(M,g)$ be a closed Riemannian manifold with $n=\dim M$, let $\xi^*\in H^1(M,\mathbb{Z}_2)$ be a flat bundle class selected by the variational principle, and let…