3 problems

Unstable relative Gromov–Lawson–Rosenberg conjecture. If the relative higher index of $D$ is zero in

Gromov's compactness conjecture. If the $\sideset{}{^1}\varprojlim$ higher index of the Dirac operator of $X$ vanishes, then $X$ admits a complete Riemannian metric with scalar cur…

Let $M$ be a compact oriented manifold whose universal covering does not admit a spin structure. Write $\Gamma=\pi_1(M)$, let $n=\dim M\ge 5$, and let … be the composition of the c…