The odd-dimensional hyperbolic virtual fibring conjecture

A finite-volume hyperbolic manifold is a quotient of real hyperbolic space by a group of isometries acting freely and properly discontinuously. Odd-dimensional hyperbolic virtual fibring conjecture. Every finite-volume hyperbolic manifold of odd dimension is virtually fibred.

The claim is motivated by virtual fibering in dimension $3$, the existence of a $5$-dimensional finite-volume hyperbolic example that fibres, and vanishing results for $L^2$-homology in odd dimensions. The source describes the evidence as scant and leaves the conjecture open.