4-manifolds are quotients of \(\mathbb{R}^4\) (Q1568690)

Let \(M\) be an \(n\)-dimensional manifold whose universal covering is \(\mathbb{R}^n\). Then \(M\) is homeomorphic to the quotient space of \(\mathbb{R}^n\) by the group \(G\cong\pi_1(M)\) of covering transformations. The 2-sphere has universal cover itself again; but it is still true that the 2-sphere is a quotient of the real Euclidean plane by a group of homeomorphisms since the 2-fold branched covering of a 2-sphere is a torus. So a natural question arises, that is: Are all connected manifolds quotients of Euclidean spaces? Of course, this is true for dimension \(\leq 2\) where the three-dimensional case is due to \textit{M. Sakuma} [Math. Semin. Notes, Kobe Univ. 9, 159-180 (1981; Zbl 0483.57003)] for the orientable case, and successively to Cooper and the author (see Theorem 2.2 and Theorem 5.7) for the general case, using techniques developed in the quoted paper. However, the main result of the author is the four-dimensional case. More precisely, he proves that every connected piecewise linear 4-manifold is PL homeomorphic to a quotient of \(\mathbb{R}^4\) by a group of PL homeomorphisms (Theorem 1.1).