How different is the universal cover of a given finite 2-complex from a
3-manifold (from the proper homotopy viewpoint)? Regarding this question, we
recall that a finitely presented group $G$ is said to be properly 3-realizable
if there exists a compact 2-polyhedron $K$ with $\pi_1(K) \cong G$ whose
universal cover $\tilde{K}$ has the proper homotopy type of a PL 3-manifold
(with boundary).
How different is the universal cover of a given finite 2-complex from a
3-manifold (from the proper homotopy viewpoint)? Regarding this question, we
recall that a finitely presented group $G$ is said to be properly 3-realizable
if there exists a compact 2-polyhedron $K$ with $\pi_1(K) \cong G$ whose
universal cover $\tilde{K}$ has the proper homotopy type of a PL 3-manifold
(with boundary).