Singer conjecture for closed aspherical manifolds

Let $M$ be a closed aspherical $n$-manifold. Singer's conjecture. The $ell^2$-Betti numbers satisfy

$$b^{(2)}_p(\widetilde{M};\pi_1 M)=0$$

for all $p\neq n/2$. The Singer conjecture is a major unresolved problem concerning $ell^2$-Betti numbers and the topology of manifolds; the surrounding results provide consequences relating BNSR invariants to its validity.