Ščepin's local triviality conjecture for Serre fibrations with low-dimensional manifold fibers

Let $p\colon E\to B$ be a Serre fibration of metric spaces, where $B$ is locally arcwise connected, and suppose that every fiber of $p$ is homeomorphic to a given manifold $M^n$ of dimension $n\leq 4$. Ščepin's conjecture. The fibration $p$ is locally trivial. This extends the known one-dimensional case and concerns when Serre fibrations with manifold fibers are actually locally trivial; the supplied text does not indicate whether the assertion has been resolved.