4 problems

Vanishing conjecture for higher localised $\widehat{A}$-genera. If $M$ admits a $\Gamma$-invariant Riemannian metric of positive scalar curvature, then for every closed $m$-form…

Let a finitely generated discrete group $\Gamma$ act properly on a spin manifold $M$. In the cocompact case, the higher localised $\widehat{A}$-genera are the invariants obtained b…

Positive-scalar-curvature moduli rank conjecture. The rank of $\widetilde P(M)$ satisfies

Let $\widetilde{D}_M$ be an $L^2$-invertible $\Gamma$-equivariant Dirac operator on a Galois $\Gamma$-covering $\widetilde{M}\to M$, acting on sections of a $\Gamma$-equivariant co…