Cell-like resolutions of polyhedra by special ones
Dusan D. Repovs, Arkady Skopenkov · Colloquium Mathematicum · 2000
Suppose that P is a finite 2-polyhedron. We prove that there exists a PL surjective map f:Q → P from a fake surface Q with preimages of f either points or arcs or 2-disks. This yields a reduction of the Whitehead asphericity conjecture (which asserts that